diff --git a/.github/workflows/python.yaml b/.github/workflows/python.yaml index 62355b4..2cc81cd 100644 --- a/.github/workflows/python.yaml +++ b/.github/workflows/python.yaml @@ -1,6 +1,11 @@ name: Python package -on: [push] +on: + pull_request: + paths: + - "neurallogic/**" + - "tests/**" + - ".github/workflows/**" jobs: build: diff --git a/README.md b/README.md index d76f20c..8e75262 100644 --- a/README.md +++ b/README.md @@ -1,45 +1,52 @@ -# differentiable-boolean-logic-networks +# ∂B nets -[![Python package](https://github.com/github/neural-logic/actions/workflows/python.yaml/badge.svg)](https://github.com/github/neural-logic/actions/workflows/python.yaml) +[![Python package](https://github.com/Z80coder/discrete-differentiable-networks/actions/workflows/python.yaml/badge.svg)](https://github.com/Z80coder/discrete-differentiable-networks/actions/workflows/python.yaml) -[![Open in GitHub Codespaces](https://github.com/codespaces/badge.svg)](https://z80coder-legendary-space-cod-65vqgjqqxjq2xv44.github.dev/) +A neural network library for learning boolean-valued, discrete functions on GPUs with gradient descent. -A Boolean Logic Network library for learning boolean functions on GPUs with gradient descent. - -The working prototype is implemented in Wolfram. The production library is implemented in Python. +The library is implemented in Python using the [Flax](https://github.com/google/flax) and [JAX](https://github.com/google/jax) frameworks. Questions? Ask @Z80coder -

- -

+## Papers + +[Lossless hardening with ∂𝔹 nets](https://differentiable.xyz/papers/paper_21.pdf). I. Wright. In ["Differentiable Almost Everything: Differentiable Relaxations, Algorithms, Operators, and Simulators"](https://differentiable.xyz/papers), ICML 2023 Workshop, Honolulu, 2023. + +Draft paper: ["∂B nets: learning discrete functions by gradient descent"](https://arxiv.org/abs/2305.07315) (April 2023). ## Demos -Neural logic nets +[Neural network research with the Wolfram language](https://youtu.be/FeIwI49AEgM?si=HCOAFOTLHmFmwOXn) (30 mins). + +[∂B nets quick overview](https://drive.google.com/file/d/1wi0uCpCgdSSlyXlb1XmzeE_u7adugAEa/view?usp=sharing) (30 mins). + +[∂B nets overview](https://drive.google.com/file/d/1UUhv6loBrFnZ7jwiHBofnp06at_8bm_F/view?usp=share_link) (1 hour). + +## Prototype + +The working prototype was implemented in Wolfram. The demos below were snapshots of work-in-progress. -https://user-images.githubusercontent.com/55286208/205712875-54d4cdfe-5199-4429-a438-3b797e4c4456.mp4 +### Prototype demos +- [Neural logic nets](https://drive.google.com/file/d/1_IECuI0f58o_aIIdaQhRo6qPH517YaMa/view?usp=share_link) (15m) -- [Neural logic nets for differentiable QL](https://drive.google.com/file/d/195r9Y08Q61V80f2Hqw62YuHpYsCzJCmZ/view?usp=sharing) (30m) -- [Boolean logic nets and MNIST](https://drive.google.com/file/d/1dWAQfFWcOm1ORqfh62H66nigGy2wQ17G/view?usp=share_link) (18m) +### Prototype development snapshots -## Development videos +- [The Soft-NOT operator](https://drive.google.com/file/d/1z2WFpz4eWLb9xauRnIl6mSXhkbU-XR6X/view?usp=share_link) (10m) +- [The Soft-AND operator](https://drive.google.com/file/d/1l9Y2cWJYYdYSsgqwfH-Dfo2Nxmiewia-/view?usp=share_link) (10m) +- [The differentiable Hard-AND operator](https://drive.google.com/file/d/1Bg1KjKF8KZaBP6jYFhQ5oARrcZYx2O8S/view?usp=share_link) (17m) +- [The differentiable Hard-OR operator](https://drive.google.com/file/d/1WUmJHToU0hQo0YgHlhJb12qECDKzmE8f/view?usp=share_link) (5m) +- [The differentiable Hard-MAJORITY operator](https://drive.google.com/file/d/18oQWhNvbkJGZ49OcQEqGAxkskGZV0e09/view?usp=share_link) (13m) +- [The hardening layer](https://drive.google.com/file/d/1c5K77n9dftsyciq32T7SBBa0PBhIgEq7/view?usp=share_link) (11m) +- [The hardening operation](https://drive.google.com/file/d/1JWA9P9BbfEHWiDfNKVjaH_ssP6CA19Nf/view?usp=share_link) (19m) +- [A classifier architecture](https://drive.google.com/file/d/1KZp8-7hbc_5tHESgmcyBDdBbZDu9UEO9/view?usp=share_link) (20m) +- [Neural logic nets](https://drive.google.com/file/d/1_IECuI0f58o_aIIdaQhRo6qPH517YaMa/view?usp=share_link) (15m) +- [Learning XOR (parity)](https://drive.google.com/file/d/1I2H3iQjM7tNrG83DJFFngQZB_T8jM6uw/view?usp=share_link) (10m) +- [Numerical regression](https://drive.google.com/file/d/1Qx9hBR2nZVymJr3Yoi1CGdg9y8VBxn8P/view?usp=share_link) (23m) +- [If-Then-Else neuron](https://drive.google.com/file/d/1siMqbLr9VYCOwBqNUAnQse9IQSGUjlqo/view?usp=share_link) (23m) +- [Neural conditions and actions](https://drive.google.com/file/d/1WH319bwV55858TYQ9G3C4RPxzdTiA0Ru/view?usp=share_link) (24m) +- [Neural decision lists](https://drive.google.com/file/d/1H0tJtiHz3yXZ7E2xeauaNRd4rnBTUf2v/view?usp=share_link) (15m) +- [Boolean logic nets and MNIST](https://drive.google.com/file/d/12Rwx8H76UTNRdBK4WAwe_QeTWiGrbP-_/view?usp=share_link) (18m) +- [Neural logic nets for differentiable QL](https://drive.google.com/file/d/15rAagCh7LxEN0CHVNkTY6iPWSxrAG0pW/view?usp=share_link) (30m) -- [The Soft-NOT operator](https://drive.google.com/file/d/1C9egUO9SWSXba7VEqqUPfECYXeLFf5g0/view?usp=sharing) (10m) -- [The Soft-AND operator](https://drive.google.com/file/d/133U60sUh4qzjrieZyMfEzULsZJF27lov/view?usp=sharing) (10m) -- [The differentiable Hard-AND operator](https://drive.google.com/file/d/1cdfMkO0xg-IUYK3avHqfarLJRXGtWcRf/view?usp=sharing) (17m) -- [The differentiable Hard-OR operator](https://drive.google.com/file/d/1v1WMfOWx4PQbjyoPJo82QNh2DGBhM4uH/view?usp=sharing) (5m) -- [The differentiable Hard-MAJORITY operator](https://drive.google.com/file/d/1qVTAFAVZ3Qlk_mYh2wd83uME89RsBzri/view?usp=sharing) (13m) -- [The hardening layer](https://drive.google.com/file/d/1ZEd34UMyFY52_0U2-j58hKJ5uvJBYREn/view?usp=sharing) (11m) -- [The hardening operation](https://drive.google.com/file/d/1M11ovLCbqAfjplFioKpMmX1hOvpwSHXv/view?usp=sharing) (19m) -- [A classifier architecture](https://drive.google.com/file/d/1sQHyo4OjapEj3a0JLhnSYEsLMBMUZMT8/view?usp=sharing) (20m) -- [Neural logic nets](https://drive.google.com/file/d/1P25OxM7Af8ppUGOUhKd6psGHI0OVXIzw/view?usp=sharing) (15m) -- [Learning XOR (parity)](https://drive.google.com/file/d/1kBxJCkuEzbisWhUGJZ42o-m6xYOZ56pB/view?usp=sharing) (10m) -- [Numerical regression](https://drive.google.com/file/d/1k2wQIjTN0omKuaFYQHrusMRIdDxPlSAf/view?usp=sharing) (23m) -- [If-Then-Else neuron](https://drive.google.com/file/d/1qelfWX6s2XhlHxFwUSV76tAS2tyDK3Q0/view?usp=sharing) (23m) -- [Neural conditions and actions](https://drive.google.com/file/d/1nrn_4TlNCmdC1ZAlN9pKIOF2hEjtykuo/view?usp=sharing) (24m) -- [Neural decision lists](https://drive.google.com/file/d/16F_2kpBaZO-qPQLX38Sar9pJfuunsVyO/view?usp=sharing) (15m) -- [Boolean logic nets and MNIST](https://drive.google.com/file/d/1dWAQfFWcOm1ORqfh62H66nigGy2wQ17G/view?usp=share_link) (18m) -More to come! diff --git a/demos/margin-and.nb b/demos/margin-and.nb new file mode 100644 index 0000000..a3a8679 --- /dev/null +++ b/demos/margin-and.nb @@ -0,0 +1,13890 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 13.2' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 825360, 13882] 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Boolean functions. + +So let's get straight into it. + +# R&D goals + +We train neural nets by iteratively adjusting their weights by backpropagating an error signal to minimize the loss on the training data. Essentially, this process performs gradient descent in a high-dimensional weight space. + +For backprop to work, neural networks must be differentiable functions. + +But this creates some problems. + +We can't learn discrete, non-differentiable functions, such as boolean functions. Discrete functions give better bias for some learning problems. + +And the nets can be huge and expensive to query, because we store and operate on floating point numbers. + +There's plenty of existing work that aims to reduce net sizes, such as weight quantization, which reduces the number of bits per weight. But quantization is a kind of lossy compression which degrades the network's predictive performance. + +So I wanted to see whether we could have our cake and eat it. + +I wanted to see whether we can define a new kind of network, which is differentiable, so we can train it efficiently with backpropoagation, but post-training convert it to an equivalent boolean function with 1-bit weights -- but without any loss of performance. + +This is the idea behind db-nets. + +Look at this diagram. + +A db-net has two aspects: a soft-net, which is differentiable, and a hard-net, which is a boolean function. We train the soft-net as normal, convert its weights to 1-bit booleans, and bind them with the boolean function. Then the boolean function behaves in exactly the same way as the soft net. + +So this is what I set out to do. I wasn't sure if it was possible. And I knew I had to rapidly explore, and test, lots and lots of ideas. + +Which is why I chose to prototype in the Wolfram language. + +# Hard and soft-bits + +Let's just start with some basics. We need to define two kinds of bits. + +A hard-bit is a boolean value. A soft-bit is a real number between 0 and 1. + +## Conversion + +A soft-bit convers to True if its greater than 1/2. Otherwise it converts to False. + +For example, this vector of soft-bits converts to a vector of hard-bits. + +## Hard equivalence + +We want the hard-net to be semantically equivalent to the soft-net. What do we mean by that? + +The LHS of this equation says: supply an input x to the soft-net and get an output. And then harden that output to hard-bits. + +The RHS says: harden the same input x, and then supply the hard-bits to the hard-net to get another output. + +If these two outputs are identical, for all possible inputs, then the soft and hard-nets are semantically equivalent. + +This is a "hard-equivalence" requirement that db-nets must satisfy. + +This requirement turned out to be surprisingly hard to satsify! I had to try lots and lots of different approaches. + +Over a period of a few months I prototyped -- no exaggeration -- 100s of ideas. + +The Wolfram Language, because its a single, unified system that provides everything immedaitely out-of-the-box, and it all works together, I essentially had a playground to try all kinds of wacky and wonderful ideas. I made extensive use of the ability to quickly dynamically visualise functions, and their gradients, to give me immediate intuition. Most ideas didn't work. But I could prototype really fast, and discard them. + +# Learning to AND + +I'll briefly explain how db-nets satisfy hard-equivalence by stepping through a simple example. + +Imagine we want a network component that can learn to mask an input x to False if a learnable weight w is False; otherwise we pass-through its value unaltered. + +Essentially, we we want to learn a boolean weight, w, for the boolean function And. + +We can see this more clearly by using the TruthTable function from the Wolfram function repository. + +[Show Truth Table, and explain logic] + +Now, logical And is not a differentiable function. So we can't simply stick it inside a neural network and expect backprop to work. + +# Product logic + +Real-valued relaxations of boolean logic already exist. For example, product logic implements logical And by multiplying soft-bits. + +How does this work? Let's use Wolfram's Manipulate functionality to see how. + +[Execute Manipulate line] + +In this plot the horizontal axis is the input x. The vertical axis is the output. And we can vary the value of the learnable weight. + +Here the weight is 1 or True, so ProductAnd should act as a pass-through. And we can see that output always equals the input. + +Now, let's set the weight to 0 or False. Now we can see that ProductAnd is entirely masking the input. The output is always 0 or False. + +So ProductAnd is acting just like logical And. + +But look what happens at intermediate values. Let's set the weight to w=0.6, which hardens to True. We want the output to high when the input is high. +But there's a region where this doesn't work. The output is less than 0.5, which hardens to False. + +So ProductAnd, in this region, is not hard-equivalent to logical And. + +That's a problem. + +Now, the output varies continuously with both the input, x, and the weight, w. So ProductAnd has a gradient everywhere, and therefore +is differentiable in the right way for backpropagation. It's a gradient-rich function. + +But it's not hard-equivalent. If we used it at training-time, and then hardened the learned weights, we'd get completly different behaviour in the hard-net. The soft-net's training wouldn't transfer to the hard-net. + +# Godel logic + +The are different relaxations of boolean logic we can try. Godel logic defines logical And in terms of Min. + +Again, let's visualise it to get some quick intuition. + +When the weight is 1 it all looks good. And when the weight is 0 it all looks good. + +Let's look at intermediate values. When the weight is 0.6 we can see that Godel And still works. +That's because when the input is high the output is also high. It respects the hard transition at 0.5 betwen soft-bits and hard-bits. + +But there's a problem! + +The Min operator essentially selects either the input value, or the weight, as its output. So any change in the unselected value doesn't change the value of the output. + +That's why the output is sometimes flat. Because any variation in the input value x has no effect on the output value. + +And that means there is no gradient. It means we can only backpropagate error through one of the inputs. And that's bad for learning. + +So Godel-And is hard-equivalent, but it isn't gradient rich. + +So this won't work either! + +# Margin packing + +We need db-nets to be composed of relaxations of logical operators that are both hard-equivalent and gradient rich. +How can we have our cake and eat it? + +My eventual solution, after prototyping lots of different approaches, is something I call margin packing. + +I'll explain it with a dynamic visualisation -- which was easy to set-up in the Wolfram Language. + +[Activate visualization] + +Here we can manipulate both the input value, x, and the weight, w. +I'll set the weight to 1 so this should act as a pass-through. + +[Set weight to w] + +We saw that Godel-And is hard-equivalent to logical And. So we'll use Godel-And to define a "representative bit", which is guaranteed to be hard-equivalent to logical And. + +The representative bit as the bold vertical line. Currently the output is 0 because the input is 0. + +[Vary x] + +But as I vary x, we can see the representative bit behave like Godel-And. The output is exactly the same as the input. + +The next thing to notice is that there's always a margin between the representative bit and the hard threshold at 1/2. + +And any output-values within the margin are guaranteed to be hard-equivalent to logical And. + +So we don't have to choose the representative bit. We can pack that margin with extra, gradient-rich information. + +In other words, we can compute an augmented-bit, which is a always function of both the input and the weight. + +So although the representative bit doesn't vary, the augmented bit does. +[Show how the agumented bit varies but the representative bit doesn't] + +The mathematical details of margin packing aren't important now. + +But we can margin-pack Godel-And to get a new, piecewise differentiable function. + +Let's visualize its behaviour again. + +We can immiediately see that this new function is both hard-equivalent with no flat gradients, and therefore gradient-rich. + +(Actually this function is differentiable almost everywhere, which is sufficient for backpropagation to work.) + +So we construct db-nets from margin-packed, differentiable analogues of boolean operators. We can compose these new differentiable +functions into multi-input neurons, then into multi-input layers, and then finally into complete net architectures. + +So let's do that. + +# Neural network layers + +I rapidly prototyped a db-nets library, building on top of Wolfram Language's neural network support. + +Wolfram's neural net functions are beautifully high-level and composable, but also give a lot of low-level control. + +So I could quickly try out lots of new ideas, and quickly test them. + +I defined layers that learn to perform different kinds of logical operations on subsets of their inputs. + +## Boolean majority + +But here we'll look at just one example, which I think is interesting, because it demonstrates the power of the Wolfram Language. + +The boolean Majority function outputs True if the majority of its inputs are True. It's a discrete analogue of a threshold function, which turns out to be very useful for learning. + +[Run examples of Majority] + +Majority can be implemented in terms of AND and ORs. + +[Show DNF form] + +However, the number of terms grows exponentially with the inputs. + +And no algorithm exists for finding the minimal boolean representation of Majority. + +In machine-learning applications we may want thousands of inputs bits to a single majority neuron. And thousands of neurons. So implementing Majority in terms of differentiable combinations of ANDs and ORs becomes explosive to compute at training time. + +So what can we do? + +Notice that if we sorted the soft-bit inputs in ascending size then the "middle bit" would be a representative bit, and therefore hard-equivalent +to boolean majority. + +Why? Because if the majority of bits are high, then the middle of the sorted list is also guaranteed to be high. + +And, remarkably, we can easily implement this logic using Wolfram's FunctionLayer and PartLayer. + +The FunctionLayer sorts the inputs, and the PartLayer picks out the "middle bit". And this is just 2 lines of Wolfram code! + +And the Wolfram Language takes care of everything, including compiling it down to differentiable code. + +You might think: how on earth can we backpropagate through a Sort algorithm? Well we're not. We're backpropagating through +the representative bit selected by a Sorting algorithm. The error is then backpropped through the representative bit. + +But we can then margin-pack this bit to backprop error through all the input bits. + +So we avoid the explosive blow-up by paying the run-time cost of Sorting. + +## Soft net + +So here's such a differentiable majority layer, which takes 8 inputs. + +Every time you define a db-net component you get 2 things: the soft-net and the corresponding hard-net. + +Let's look at the soft-net. Wolfram's out-of-the-box visualisations really help when wiring nets together. + +And it's pretty incredible how Wolfram Language just automatically wires the above 2 lines into a differentiable layer. +[Just play with visualization] + +And we can immediately test this layer, to see how it behaves. + +[Run and briefly explain the 2 lines of code] + +## Hard net + +What does the corresponding hard-net look like? + +It's just a Wolfram function (with some extra complexity we can ignore). Because really, in the insides, its just the Wolfram's built-in boolean +Majority function. +[Highlight it] + +This means, post-training, we throw away any Sorting. Instead, at query-time, we just use boolean Majority, which is extremely fast to compute +(becuase we just count bits). + +## Hard equivalence + +And we can quickly check that it behaves the same as the soft-net. + +The db-nets library exploits many different features of Wolfram's neural network support. + +For example, I use a CompiledLayer to define special neurons that behave differently in their forward and backward passes. The details aren't important. + +But what is important is that Wolfram Language allows you very deep control, which is essential for research purposes, when +you're exploring novel ideas. + +# A classification problem + +OK, let's put this all together, and demonstrate db-nets working in practice. + +Let's get a small dataset from the Wolfram data repository. + +It's a dataset describing features of cars. The aim is to predict 4 labels, one of +- unacceptable +- acceptable +- good +- or very good +which defines whether a car is worth buying. + +So this is a multi-class classification problem. With numeric and categorical features. + +# A classification problem + +Let's quickly split the data into a train and test set, using another function from the Wolfram function repository. + +We'll use a function from the Wolfram function repository to split the data into a train and test set. + +## Input encoder + +The built-in NetEncoder function make it really easy to convert the input features into an indicator vector of booleans. + +And then we compose the encoders into a single input layer. +[Show input encoder layer] +You can see that this layer convers the input features into a vector of 21 hard-bits. + +It's really cool how easy it is to do this, and visualize what's going on. + +# Define db-net + +[Just immediately run all the lines of code] + +We'll now define a complete db-net architecture to learn this classification problem. + +It has two layers, an logical OR layer, followed by a logical NOT layer. Each layer has 64 "logical" neurons, with new kinds of activation functions. + +The net has 4 output ports for each class. Each output port is a vector of bits. +We add up the bits in each port, and interpret them as relative class probabilities. + +Then we use a standard cross-entropy loss for training. + +# Train db-net + +This is now reeady to train. And training on my laptop's GPU just works out-of-the-box. + +We can see that the loss decreases. So it's definitely learning something! + +And we can stop the training at anytime. [Stop after less than a minute] + +And once trained, we can extract the trained net. + +# Evaluate db-net + +Let's quickly evaluate its performance on the test data. + +Here I use Wolfram's ClassifierMeasurements function to evaluate the soft-net. It automatically give lots of useful information. + +The confusion matrix shows that the db-net has solved this problem. In fact it seems to have got only X examples wrong. +And the estimated accuracy is about XX%. + +# Bind weights with hard-net + +But what we really want is the boolean function that predicts whether a car is acceptable or not. + +We extract it by binding the hardened trained weights from the soft-net with the corresponding hard-net. +[Run first line of code] + +What we get is a Wolfram function with associated boolean weights. This is the hard-net representation. +[Show then delete large output] + +And because this is a Wolfram function we can symbolically evaluate it to see precisely what boolean function has been learned! + +[Run second line of code] + +Here we're looking at the symbolic hard-bits that are outputted by the net on 1 of its 4 ports. +The b's correspond to the 21 inputs bits, which represents features of the car. +Each boolean expression logically combines different feature values to give 1-bit of predictive information. + +So we have learned, by backpropoagation, a boolean function that classifies cars! + +# Evaluate boolean classifier + +How does this boolean classifier peform? Well, because of hard-equivalence, it should perform identically to the soft-net + +Let's evaluate its performance on the test data. +[Run 2 lines of code] + +It gets an accuracy of 99.4%, which as you can see, is identical to the soft-net's performance. +So there is no loss of accuracy. The non-differentiable boolean function is semantically equivalent to the differentiable net. + +## Size of boolean classifier + +And we get this accuracy with a much, much smaller net at query-time. +In fact the weights for this classifier only consume 0.2 k. + +In comparison, a minimal-size MLP on this same problem consumes about 16 k. + +Also boolean and integer operations can be much cheaper than floating-point operations. +So this makes db-nets a potentially good choice when deploying ML on edge devices. + +And db-nets are not restricted to toy classification problems. We can use them for numerical regression problems. +And image recognition. In fact, anything. + +# Conclusion + +OK, let's come to a close. + +The Wolfram Language is great for rapidly prototyping new ideas. Everything works out-of-the-box and works together no problems. You don't have to think about choosing packages, or versions, or dependencies. You can immediately start working on your problem, without distractions or frustrations. + +The Neural Network support is very high-level, yet very flexible and configurable. You can work fast. + +And if you want to push what neural nets can do, and explore entirely new kinds of neural nets, then you can. + +I had to rapidly implement and evaluate 100s of ideas before solving my research problem. Without Wolfram Language I think I may have given up. But it's such a joy to use, and the gap between ideas and reality is so small, that I enjoyed every step -- even when many of my ideas failed. + +## More on db-nets + +If you want to learn more about db-nets then there's a paper published at ICML. And a GitHub repo with all the code. + +Thanks for listening! diff --git a/docs/ICML_workshop/db-icml.tex b/docs/ICML_workshop/db-icml.tex new file mode 100644 index 0000000..ad673f0 --- /dev/null +++ b/docs/ICML_workshop/db-icml.tex @@ -0,0 +1,701 @@ +%%%%%%%% ICML 2023 EXAMPLE LATEX SUBMISSION FILE %%%%%%%%%%%%%%%%% + +\documentclass{article} + +% Recommended, but optional, packages for figures and better typesetting: +\usepackage{microtype} +\usepackage{graphicx} +\usepackage{subfigure} +\usepackage{booktabs} % for professional tables + +% hyperref makes hyperlinks in the resulting PDF. +% If your build breaks (sometimes temporarily if a hyperlink spans a page) +% please comment out the following usepackage line and replace +% \usepackage{icml2023} with \usepackage[nohyperref]{icml2023} above. +\usepackage[hyphens]{url} +\usepackage{hyperref} + + +% Attempt to make hyperref and algorithmic work together better: +\newcommand{\theHalgorithm}{\arabic{algorithm}} + +% Use the following line for the initial blind version submitted for review: +%\usepackage{icml2023/icml2023} + +% If accepted, instead use the following line for the camera-ready submission: +\usepackage[accepted]{icml2023-diffxyz/icml2023-diffxyz} + +% For theorems and such +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathtools} +\usepackage{amsthm} + +% if you use cleveref.. +\usepackage[capitalize,noabbrev]{cleveref} + +\usepackage{listings} + +\lstset{basicstyle=\ttfamily\tiny} +\lstdefinestyle{mystyle}{ + keywordstyle=\bfseries, + keywords={ge,return,def,not,xor,ne}, +} +\lstset{breaklines=true} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% THEOREMS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\theoremstyle{plain} +\newtheorem{theorem}{Theorem}[section] +\newtheorem{proposition}[theorem]{Proposition} +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{corollary}[theorem]{Corollary} +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{assumption}[theorem]{Assumption} +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} + +\makeatletter +\newcommand{\tleft}{\mathrel\triangleleft} +\newcommand{\tright}{\mathrel\triangleright} +\DeclareRobustCommand{\btleft}{\mathrel{\mathpalette\btlr@\blacktriangleleft}} +\DeclareRobustCommand{\btright}{\mathrel{\mathpalette\btlr@\blacktriangleright}} + +\newcommand{\btlr@}[2]{% + \begingroup + \sbox\z@{$\m@th#1\triangleright$}% + \sbox\tw@{\resizebox{1.1\wd\z@}{1.1\ht\z@}{\raisebox{\depth}{$\m@th#1\mkern-1mu#2$}}}% + \ht\tw@=\ht\z@ \dp\tw@=\dp\z@ \wd\tw@=\wd\z@ + \copy\tw@ + \endgroup +} + +\newcommand{\citemyauthoryear}[1]{\citeauthor{#1} (\citeyear{#1})} + +% Todonotes is useful during development; simply uncomment the next line +% and comment out the line below the next line to turn off comments +%\usepackage[disable,textsize=tiny]{todonotes} +\usepackage[textsize=tiny]{todonotes} + +\usepackage{comment} + +% The \icmltitle you define below is probably too long as a header. +% Therefore, a short form for the running title is supplied here: +\icmltitlerunning{Lossless hardening with $\partial\mathbb{B}$ nets} + +\begin{document} + +\twocolumn[ +\icmltitle{Lossless hardening with $\partial\mathbb{B}$ nets} + +% It is OKAY to include author information, even for blind +% submissions: the style file will automatically remove it for you +% unless you've provided the [accepted] option to the icml2023 +% package. + +% List of affiliations: The first argument should be a (short) +% identifier you will use later to specify author affiliations +% Academic affiliations should list Department, University, City, Region, Country +% Industry affiliations should list Company, City, Region, Country + +% You can specify symbols, otherwise they are numbered in order. +% Ideally, you should not use this facility. Affiliations will be numbered +% in order of appearance and this is the preferred way. +\icmlsetsymbol{equal}{*} + +\begin{icmlauthorlist} +\icmlauthor{Ian Wright}{comp} +\end{icmlauthorlist} + +\icmlaffiliation{comp}{GitHub, Oxford, UK} + +\icmlcorrespondingauthor{Ian Wright}{wrighti@acm.org} + +% You may provide any keywords that you +% find helpful for describing your paper; these are used to populate +% the "keywords" metadata in the PDF but will not be shown in the document +\icmlkeywords{Machine Learning, ICML} + +\vskip 0.3in +] + +% this must go after the closing bracket ] following \twocolumn[ ... + +% This command actually creates the footnote in the first column +% listing the affiliations and the copyright notice. +% The command takes one argument, which is text to display at the start of the footnote. +% The \icmlEqualContribution command is standard text for equal contribution. +% Remove it (just {}) if you do not need this facility. + +%\printAffiliationsAndNotice{} % leave blank if no need to mention equal contribution +\printAffiliationsAndNotice{{}} % otherwise use the standard text. + +\begin{abstract} + $\partial\mathbb{B}$ nets are differentiable neural networks that learn discrete boolean-valued functions by gradient descent. $\partial\mathbb{B}$ nets have two semantically equivalent aspects: a differentiable soft-net, with real weights, and a non-differentiable hard-net, with boolean weights. We train the soft-net by backpropagation and then `harden' the learned weights to yield boolean weights that bind with the hard-net. The result is a learned discrete function. Unlike existing approaches to neural network binarization the `hardening' operation involves no loss of accuracy. Preliminary experiments demonstrate that $\partial\mathbb{B}$ nets achieve comparable performance on standard machine learning problems yet are compact (due to 1-bit weights) and interpretable (due to the logical nature of the learnt functions). +\end{abstract} + +\vspace{-0.96cm} + +\section{Introduction} + +Neural networks must be differentiable. But differentiability means we cannot directly learn discrete functions, such as logical predicates. We can approximate discrete functions by defining continuous relaxations. This paper explores a different approach: we define differentiable functions that `harden', without approximation, to discrete functions. + +Specifically, $\partial \mathbb{B}$ nets have two aspects: a {\em soft-net}, which is a differentiable function with real weights, and a {\em hard-net}, which is a discrete function with boolean weights. Both aspects are semantically equivalent. We train the soft-net as normal, using backpropagation, then `harden' the learned weights to boolean values, which bind with the hard-net to yield a discrete function with identical predictive performance (see Figure \ref{fig:main-idea}). + +\begin{figure}[h] + \centering + \includegraphics[trim=80pt 25pt 40pt 10pt, clip, width=0.5\textwidth]{../db-net.png} + \caption{{\em Learning discrete functions with a $\partial\mathbb{B}$ net.}} + \label{fig:main-idea} +\end{figure} + +\section{$\partial\mathbb{B}$ nets}\label{sec:db-nets} + +\begin{definition}[Soft-bits and hard-bits] + A {\em soft-bit} is a real value in the range $[0,1]$ and a {\em hard-bit} is a boolean value from the set $\{0,1\}$. A soft-bit, $x$, is {\em high} if $x>1/2$, otherwise it is {\em low}. +\end{definition} +A hardening function converts soft-bits to hard-bits. +\begin{definition}[Hardening] + The {\em hardening} function, $\operatorname{harden}(x_{1}, \dots, x_{n}) = [f(x_{1}), \dots, f(x_{n})]$, converts soft-bits to hard-bits, where $f(x)=1$ if $x > 1/2$ and $f(x)=0$ otherwise. +\end{definition} + +Soft-nets use soft-bits and hard-nets use hard-bits. A soft-net learns 1-bit weights by representing them, at training time, as real numbers. The equivalent hard-net, at inference time, simply uses 1-bit weights. +A soft-net is any differentiable, or differentiable a.e., function, $f$, that `hardens' to a hard-net that is a semantically equivalent discrete function, $g$. + +\begin{definition}[Hard-equivalence] + A function, $f: [0,1]^n \rightarrow [0,1]^m$, is {\em hard-equivalent} to a discrete function, $g: \{1,0\}^n \rightarrow \{1,0\}^m$, if $\operatorname{harden}(f({\bf x})) = g(\operatorname{harden}({\bf x}))$ + for all ${\bf x} \in \{(x_{1}, \dots, x_{n}) ~|~ x_{i} \in [0,1] \setminus \{1/2\}\}$. For shorthand write $f \btright g$. +\end{definition} + +$\partial \mathbb{B}$ nets are composed from `activation' functions that are hard-equivalent to boolean functions (and natural generalisations). + +\subsection{Learning to negate} + +Say we aim to learn to negate a boolean value, $x$, or leave it unaltered. Represent this decision by a boolean weight, $w$, where low $w$ means negate and high $w$ means do not. The boolean function that meets this requirement is $\neg(x \oplus w)$. However, this function is not differentiable. Define the differentiable function, +$\partial_{\neg}(w, x) = 1 - w + x (2w - 1)$, +where $\partial_{\neg}(w, x) \btright \neg(x \oplus w)$ (see proposition \ref{prop:not}). + +Many kinds of differentiable fuzzy logic operators exist (see \citemyauthoryear{VANKRIEKEN2022103602} for a review). So why this functional form? Product logics, where $f(x,y) = x y$ is as a soft version of $x \wedge y$, although hard-equivalent at extreme values, e.g. $f(1,1)=1$ and $f(0,1)=0$, are not hard-equivalent at intermediate values, e.g. $f(0.6, 0.6) = 0.36$, which hardens to $\operatorname{False}$ not $\operatorname{True}$. G\"{o}del-style $\operatorname{min}$ and $\operatorname{max}$ functions, although hard-equivalent over the entire soft-bit range, i.e. $\operatorname{min}(x,y) \btright x \wedge y$ and $\operatorname{max}(x,y) \btright x \vee y$, are gradient-sparse in the sense that their outputs do not always vary when any input changes, e.g. $\frac{\partial}{\partial x} \operatorname{max}(x,y) = 0$ when $(x,y)=(0.1, 0.9)$. So although the composite function $\operatorname{max}(\operatorname{min}(w, x), \operatorname{min}(1-w, 1-x))$ is differentiable and $\btright \neg(x \oplus w)$ it does not always backpropagate error to its inputs. In contrast, $\partial_{\neg}$ always backpropagates error to its inputs because it is a gradient-rich function (see Figure \ref{fig:gradient-rich}). + +\begin{definition}[Gradient-rich] + A function, $f: [0,1]^n \rightarrow [0,1]^m$, is {\em gradient-rich} if $\frac{\partial f({\bf x})}{\partial x_{i}} \neq {\bf 0}$ for all ${\bf x} \in \{(x_{1}, \dots, x_{n}) ~|~ x_{i} \in [0,1] \setminus \{1/2\}\}$. +\end{definition} + +$\partial \mathbb{B}$ nets are composed of hard-equivalent `activation' functions that are, where possible, gradient-rich. To meet this requirement we introduce the technique of margin packing. + +\subsection{Margin packing} + +\begin{figure}[t!] + \centering + \includegraphics[trim=30pt 5pt 30pt 10pt, clip, width=.49\textwidth]{../margin-trick.png} + \caption{{\em Margin packing for constructing gradient-rich, hard-equivalent functions}. A representative bit, $z$, is hard-equivalent to a discrete target function but gradient-sparse (e.g. $z=\operatorname{min}(x,y) \btright x \wedge y$). On the left $z$ is low, $z<1/2$; on the right $z$ is high, $z>1/2$. We can pack a fraction of the margin between $z$ and the hard threshold $1/2$ with additional gradient-rich information without affecting hard-equivalence. A natural choice is the mean soft-bit, $\bar{\bf x} \in [0,1]$. The grey shaded areas denote the packed margins and the final augmented bit. On the left $\approx 60\%$ of the margin is packed; on the right $\approx 90\%$.} + \label{fig:margin-trick} +\end{figure} +% On the left, ${\bf x}=[0.9,0.23]$, $z=0.23$, $\bar{\bf x}=0.57$ and therefore $\approx 60\%$ of the margin is packed; on the right, ${\bf x}=[0.9,0.83]$, $z=0.83$, $\bar{\bf x}=0.87$, and therefore $\approx 90\%$ of the margin is packed. + +Say we aim to construct a differentiable analogue of $x \wedge y$. Note that $\operatorname{min}(x,y)$ essentially selects one of $x$ or $y$ as a representative soft-bit that is guaranteed hard-equivalent to $x \wedge y$. However, by selecting only one of $x$ or $y$ then $\operatorname{min}$ is also guaranteed to be gradient-sparse. We define a `margin packing' method to solve this dilemma. + +The main idea of margin packing is (i) select a representative bit that is hard-equivalent to the target discrete function, and then (ii) pack a fraction of the margin between the representative bit and the hard threshold $1/2$ with gradient-rich information. The result is an augmented bit that is a function of all inputs yet hard-equivalent to the target function. More concretely, say a vector of soft-bit inputs ${\bf x}$ has an $i$th element that represents the target discrete function (e.g. if our target is $x \wedge y$ then ${\bf x}=[x,y]$ and $i$ is 1 if $x 1/2 \\ +x_{i} + \operatorname{margin-fraction}({\bf x}, i) & \text{otherwise,} +\end{cases} +\end{aligned} +\label{eq:augmented-bit} +\end{equation} +which is differentiable a.e. Note that if the representative bit is high (resp. low) then the augmented bit is also high (resp. low). The difference between the augmented and representative bit depends on the size of the available margin and the mean soft-bit value. Almost everywhere, an increase (resp. decrease) of the mean soft-bit increases (resp. decreases) the value of the augmented bit (see Figure \ref{fig:margin-trick}). Note that if the $i$th bit is representative (i.e. hard-equivalent to the target function) then so is the augmented bit (see lemma \ref{prop:augmented}). We use margin packing, where appropriate, to define gradient-rich, hard-equivalents of boolean functions. + +\subsection{Differentiable $\wedge$, $\vee$ and $\Rightarrow$} + +\begin{figure*}[t!] + \centering + \includegraphics[trim=0pt 0pt 0pt 0pt, clip, width=0.8\textwidth]{../logic-gates.png} + \caption{{\em Gradient-rich versus gradient-sparse differentiable boolean functions.} Each column contains contour plots of functions $f(x,y)$ that are hard-equivalent to a boolean function (one of $\neg(x \oplus y)$, $x \wedge y$, $x \vee y$, or $x \Rightarrow y$). Every function is continuous and differentiable a.e. (white lines indicate non-continuous derivatives). The upper plots are gradient-sparse, where vertical and horizontal contours indicate the function is constant with respect to one of its inputs, i.e. $\partial f/\partial y = 0$ or $\partial f/\partial x = 0$. The lower plots are gradient-rich, where the curved contours indicate the function always varies with respect to any of its inputs, i.e. $\partial f/\partial y \neq 0$ and $\partial f/\partial x \neq 0$. $\partial \mathbb{B}$ nets use gradient-rich functions to ensure that error is always backpropagated to all inputs.} + \label{fig:gradient-rich} +\end{figure*} + +We aim to construct a differentiable analogue of the boolean function $\bigwedge_{i=1}^{n} x_i$. A representative bit is $\operatorname{min}(x_{1},\dots,x_{n})$. The function +$\partial_{\wedge}({\bf x}) = \operatorname{augmented-bit}({\bf x}, \operatorname{argmin}\limits_{i} x[i])$ +is therefore hard-equivalent to the boolean function $\bigwedge_{i=1}^{n} x_i$ (see proposition \ref{prop:and}). In the special case $n=2$ we get the piecewise function, +$\partial_{\wedge}\!(x, y) = 1/2 + 1/2(x + y)(\operatorname{min}(x,y) - 1/2)$ if $\operatorname{min}(x,y) > 1/2$, and $\partial_{\wedge}\!(x, y) = \operatorname{min}(x,y) + 1/2(x + y)(1/2 - \operatorname{min}(x,y))$ +otherwise. Note that $\partial_{\wedge}$ is differentiable a.e. and gradient-rich (see Figure \ref{fig:gradient-rich}). The differentiable analogue of $\vee$ is identical to $\wedge$, except the representative bit is selected by $\operatorname{max}$. The function +$\partial_{\vee}({\bf x}) = \operatorname{augmented-bit}({\bf x}, \operatorname{argmax}\limits_{i} x[i])$ is hard-equivalent to the boolean function $\bigvee_{i=1}^{n} x_i$ (see proposition \ref{prop:or}) (see Figure \ref{fig:gradient-rich}). +The differentiable analogue of $\Rightarrow$ (material implication) is defined in terms of $\partial_{\vee}$. The function +$\partial_{\Rightarrow}(x, y) = \partial_{\vee}\!(y, 1-x)$, +is hard-equivalent to $x \Rightarrow y$ (see proposition \ref{prop:implies}). We can define analogues of all the basic boolean operators in a similar manner. + +\subsection{Differentiable majority} + +\begin{figure*}[t] + \centering + \includegraphics[trim=0pt 0pt 0pt 0pt, clip, width=0.8\textwidth]{../majority-gates.png} + \caption{{\em Differentiable boolean majority.} The boolean majority function for three variables in DNF form is $\operatorname{Maj}(x,y,z) = (x \wedge y) \vee (x \wedge y) \vee (y \wedge z)$. The upper row contains contour plots of $f(x,y,z) = \operatorname{min}(\operatorname{max}(x,y), \operatorname{max}(x,z), \operatorname{max}(y,z))$ for values of $z \in \{0.2, 0.4, 0.6, 0.8\}$. $f$ is differentiable and $\btright\!\operatorname{Maj}$ but gradient-sparse (vertical and horizontal contours indicate constancy with respect to an input). Also, the number of terms in $f$ grows exponentially with the number of variables. The lower row contains contour plots of $\partial\!\operatorname{Maj}(x,y,z)$ for the same values of $z$. $\partial\!\operatorname{Maj}$ is differentiable and $\btright\!\operatorname{Maj}$ yet gradient-rich (curved contours indicate variability with respect to any inputs). In addition, the number of terms in $\partial\!\operatorname{Maj}$ is constant with respect to the number of variables.} + \label{fig:majority-plot} +\end{figure*} + +The boolean majority function is particularly important for tractable learning because it is a threshold function: +\begin{equation*} +\begin{aligned} +\operatorname{Maj}({\bf x}) &= \left\lfloor +\frac{1}{2} + \frac{\sum_{i=1}^{n} x_{i} - 1/2}{n} +\right\rfloor\text{,} +\end{aligned} +\end{equation*} +where we count $\operatorname{False}$ as $0$ and $\operatorname{True}$ as $1$. We aim to construct a differentiable analogue of $\operatorname{Maj}$. + +$\operatorname{Maj}$ for $n$ bits in DNF form is a disjunction of $\binom{n}{k}$ conjunctive clauses of size $k$, where $k=\lceil n/2 \rceil$. In principle we can implement a differentiable analogue of $\operatorname{Maj}$ in terms of $\partial_{\wedge}$ and $\partial_{\vee}$. However, the number of terms grows exponentially with the variables. No general algorithm exists to find the minimal representation of $\operatorname{Maj}$ for arbitrary $n$. Instead, we trade-off time for memory costs. Assume that the function $\operatorname{sort}({\bf x})$ sorts the elements of ${\bf x}$ in ascending order. Then the `median' soft-bit, +$\operatorname{majority-index}({\bf x}) = \lceil \frac{|{\bf x}|}{2} \rceil$, +is representative. Applying margin packing, define the differentiable function +$\partial\!\operatorname{Maj}({\bf x}) = \operatorname{augmented-bit}(\operatorname{sort}({\bf x}), \operatorname{majority-index}({\bf x}))$, +which is hard-equivalent to $\operatorname{Maj}$ (see theorem \ref{prop:majority}). Note that $\partial\!\operatorname{Maj}$ is differentiable a.e. and gradient-rich (see Figure \ref{fig:majority-plot}). If $\operatorname{sort}$ is quicksort then the average time-complexity of $\partial\!\operatorname{Maj}$ is $\mathcal{O}(n\log{}n)$, which makes $\partial\!\operatorname{Maj}$ more expensive than $\partial_{\neg}$, $\partial_{\wedge}$, $\partial_{\vee}$ and $\partial_{\Rightarrow}$ at training time. The $\operatorname{sort}$ operation could be replaced by the Floyd-Rivest algorithm, which has linear average time complexity \cite{KIWIEL2005214}. However, in the hard $\partial\mathbb{B}$ net we efficiently implement $\operatorname{Maj}$ as a discrete program that simply checks if the majority of bits are high. Note that we use $\operatorname{sort}$ to define a differentiable function that is exactly equivalent to a discrete function (rather than defining a continuous approximation to sorting, e.g. \citemyauthoryear{NEURIPS2019_d8c24ca8}, \citemyauthoryear{grover2018stochastic} and \citemyauthoryear{petersen2022monotonic}). + +We apply this methodology to construct functions that harden to other kinds of boolean functions, such as boolean counting (see Section \ref{sec:counting}). This basic set of functions is sufficient to learn non-trivial relationships from data. $\partial\mathbb{B}$ net layers are compositions of these functions, where composition preserves hard-equivalence (see Sections \ref{sec:layers} and \ref{sec:classification}). + +\section{Learning discrete functions}\label{sec:discrete} + +We briefly illustrate the kind of discrete program that $\partial\mathbb{B}$ nets can learn. Consider the toy problem of predicting whether a person wears a $\operatorname{t-shirt}$ (label 0) or a $\operatorname{coat}$ (label 1) conditional on 5 boolean features (see Table \ref{tab:toy2}). + +\begin{table}[h!] + \centering + \begin{tabular}{|c|c|c|c|c|c|} + $\text{\small very-cold}$ & $\text{\small cold}$ & $\text{\small warm}$ & $\text{\small very-warm}$ & $\text{\small outside}$ & $\text{\small label}$ \\ \hline + 1 & 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 \\ + \dots & \dots & \dots & \dots & \dots & \dots + \end{tabular} + \caption{A toy learning problem} + \label{tab:toy2} +\end{table} + +We train the $\partial\mathbb{B}$ net described in Figure 5\ref{fig:toy-example-architecture}. Once trained we harden the net to a discrete program (see Section \ref{sec:discrete}) that generates 2 hard-bits, corresponding to each label. The program symbolically simplifies to: + +\begin{lstlisting}[language=Python,style=mystyle,frame=single] +def dbNet(very-cold, cold, warm, very-warm, outside): +return [ +4 !very-cold + 4 !cold + (3 warm + !warm) + (very-warm + 3 !very-warm) + (outside + 3 !outside) >= 11, +(very-cold + 3 !very-cold) + 4 cold + 4 !warm + (3 very-warm + !very-warm) + 2 (outside + !outside) >= 11 +] +\end{lstlisting} + +Note that the program linearly weights multiple pieces of evidence due to the presence of the $\partial\!\operatorname{Maj}$ operator (overkill for this toy problem). We can read-off that the $\partial\mathbb{B}$ net has learned `if not $\operatorname{very-cold}$ and not $\operatorname{cold}$ and not $\operatorname{outside}$ then wear a $\operatorname{t-shirt}$'; and `if $\operatorname{cold}$ and not ($\operatorname{warm}$ or $\operatorname{very-warm}$) and $\operatorname{outside}$ then wear a $\operatorname{coat}$' etc. Section \ref{sec:experiments} compares $\partial\mathbb{B}$ net performance against other classification algorithms on standard machine learning problems. + +\section{Related work} + +Binary neural networks, e.g. \citemyauthoryear{10.5555/2969442.2969588}, reduce real weights and/or activations to binary, saving model size and inference costs. The binarization step is lossy, which loses accuracy \citep{QIN2020107281}. Deep differentiable logic gate networks \citep{NEURIPS2022_0d3496dd} consist of 2-input neurons arranged in a fixed topology. Each neuron learns a differentiable probability distribution over the 16 possible binary functions. Post-training the neurons are discretized to the most probable binary function. This step is lossy, which loses accuracy. $\partial\mathbb{B}$ nets aim to explore the design space of differentiable nets that enable lossless hardening. + +\section{Conclusion}\label{sec:conclusion} + +$\partial\mathbb{B}$ nets are differentiable nets that are hard-equivalent to non-differentiable, boolean-valued functions. $\partial\mathbb{B}$ nets can therefore learn discrete functions by gradient descent. Ensuring hard-equivalence requires defining new kinds of activation functions and network layers. `Margin packing' is a potentially general technique for constructing differentiable functions that are hard-equivalent yet gradient-rich. An advantage of $\partial\mathbb{B}$ nets is that `hardening' to 1-bit weights has provably identical accuracy. At inference time $\partial\mathbb{B}$ nets are highly compact and potentially cheap to evaluate. Preliminary experiments demonstrate that $\partial\mathbb{B}$ nets achieve comparable performance to existing approaches. + +% Acknowledgements should only appear in the accepted version. +\section*{Acknowledgements} +GitHub Next sponsored this research. Thanks to Pavel Augustinov, Richard Evans, Johan Rosenkilde, Max Schaefer, Ganesh Sittampalam, Tam\'{a}s Szab\'{o}, Albert Ziegler and the anonymous referees for helpful discussions and feedback. + +\bibliography{../db.bib} +\bibliographystyle{icml2023/icml2023} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% APPENDIX +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newpage +\appendix +\onecolumn + +\section{Boolean logic layers}\label{sec:layers} + +The full variety of $\partial\mathbb{B}$ net architectures is to be explored. Here we define basic layers sufficient for the classification experiments. + +A $\partial_{\neg} \!\operatorname{Layer}$ of width $n$ learns to negate up to $n$ different subsets of the elements of its input vector: +\begin{equation*} +\begin{aligned} +& \partial_{\neg} \!\operatorname{Layer}: [0,1]^{n \times m} \times [0,1]^{m} \to [0,1]^{n \times m}, \\ +({\bf W}, {\bf x}) &\mapsto +\begin{bmatrix} +\partial_{\neg}(w_{1,1}, x_{1}) & \dots & \partial_{\neg}(w_{1,m}, x_{m}) \\ +\vdots & \ddots & \vdots \\ +\partial_{\neg}(w_{n,1}, x_{1}) & \dots & \partial_{\neg}(w_{n,m}, x_{m}) +\end{bmatrix} +\end{aligned} +\end{equation*} +where ${\bf x}$ is a soft-bit input vector, ${\bf W}$ is a weight matrix and $n$ is the layer width. Similarly, A $\partial_{\Rightarrow} \!\operatorname{Layer}$ of width $n$ learns to `mask to true or $\operatorname{nop}$' up to $n$ different subsets of the elements of its input vector: +\begin{equation*} +\partial_{\Rightarrow} \!\operatorname{Layer}({\bf W}, {\bf x}) = +\begin{bmatrix} +\partial_{\Rightarrow}(w_{1,1}, x_{1}) & \dots & \partial_{\Rightarrow}(w_{1,m}, x_{m}) \\ +\vdots & \ddots & \vdots \\ +\partial_{\Rightarrow}(w_{n,1}, x_{1}) & \dots & \partial_{\Rightarrow}(w_{n,m}, x_{m}) +\end{bmatrix}\text{.} +\end{equation*} +A $\partial_{\wedge}\!\operatorname{Neuron}$ learns to logically $\wedge$ a subset of its input vector: +\begin{equation*} +\begin{aligned} +& \partial_{\wedge}\!\operatorname{Neuron}: [0,1]^{n} \times [0,1]^{n} \to [0,1], \\ +({\bf w}, {\bf x}) & \mapsto \min(\partial_{\Rightarrow}\!(w_{1}, x_{1}), \dots, \partial_{\Rightarrow}\!(w_{n}, x_{n}))\text{,} +\end{aligned} +\end{equation*} +where ${\bf w}$ is a weight vector. Each $\partial_{\Rightarrow}(w_{i},x_{i})$ learns to include or exclude $x_{i}$ from the conjunction depending on weight $w_{i}$. For example, if $w_{i}>0.5$ then $x_{i}$ affects the value of the conjunction since $\partial_{\Rightarrow}(w_{i},x_{i})$ passes-through a soft-bit that is high if $x_{i}$ is high, and low otherwise; but if $w_{i} \leq 0.5$ then $x_{i}$ does not affect the conjunction since $\partial_{\Rightarrow}(w_{i},x_{i})$ always passes-through a high soft-bit. A $\partial_{\wedge}\!\operatorname{Layer}$ of width $n$ learns up to $n$ different conjunctions of subsets of its input (of whatever size). A $\partial_{\vee}\!\operatorname{Neuron}$ is defined similarly: +\begin{equation*} +\begin{aligned} +& \partial_{\vee}\!\operatorname{Neuron}: [0,1]^{n} \times [0,1]^{n} \to [0,1], \\ +({\bf w}, {\bf x}) &\mapsto \max(\partial_{\wedge}\!(w_{1}, x_{1}), \dots, \partial_{\wedge}\!(w_{n}, x_{n}))\text{.} +\end{aligned} +\end{equation*} +Each $\partial_{\wedge}(w_{i},x_{i})$ learns to include or exclude $x_{i}$ from the disjunction depending on weight $w_{i}$. A $\partial_{\vee}\!\operatorname{Layer}$ of width $n$ learns up to $n$ different disjunctions of subsets of its input (of whatever size). +%For example, if $w_{i}>0.5$ then $x_{i}$ affects the value of the conjunction because $\partial_{\wedge}(w_{i},x_{i})$ passes-through a soft-bit that is high if $x_{i}$ is high, and low otherwise; but if $w_{i} \leq 0.5$ then $x_{i}$ does not affect the conjunction because $\partial_{\Rightarrow}(w_{i},x_{i})$ always passes-through a low soft-bit. + +We can compose $\partial_{\neg}$, $\partial_{\wedge}$ and $\partial_{\vee}$ layers to learn boolean formulae of arbitrary width and depth. + +\section{Classification layers}\label{sec:classification} + +In classification problems the final layer of a neural network is typically interpreted as a vector of real-valued logits, one for each label, where the index of the maximum logit indicates the most probable label. However, we cannot interpret a soft-bit vector as logits without violating hard-equivalence. In addition, when training $\partial\mathbb{B}$ nets, loss functions should be a function of hardened bits, otherwise gradient descent may non-optimally traverse trajectories that take no account of the hard threshold at $1/2$. For example, consider that an instance is correctly classified by a 1-hot vector with high bit $x=0.51$. Updating the net's weights to change this value to $0.51+\epsilon$ will not improve accuracy and may prevent the correct classification of a different instance. + +For these reasons, $\partial\mathbb{B}$ nets have a final `hardening' layer to ensure that loss is a function of hard, not soft, bits: +\begin{equation*} +\begin{aligned} +\partial\!\operatorname{harden}: [0,1]^{n} &\to [0,1]^{n}, \\ +{\bf x} &\mapsto \operatorname{harden}({\bf x})\text{.} +\end{aligned} +\end{equation*} +The $\operatorname{harden}$ function is not differentiable and therefore $\partial\!\operatorname{harden}$ uses the straight-through estimator \cite{DBLP:journals/corr/BengioLC13} during backpropagation. By restricting the use of the straight-through estimator to final layers we avoid compounding gradient estimation errors to deeper parts of the network. Note that $\partial\!\operatorname{harden}$ is hard-equivalent to a $\operatorname{nop}$. + +$\partial\mathbb{B}$ nets can re-use many of the techniques deployed in standard neural networks. For example, for improved generalisation, we define a `boolean' analogue of the dropout layer \cite{JMLR:v15:srivastava14a}: +\begin{equation*} +\begin{aligned} +\partial\!\operatorname{dropout}: [0,1]^{n} \times [0,1] &\to [0,1]^{n}, \\ +({\bf x}, p) &\mapsto [f(x_{1}, p), \dots, f(x_{n}, p)]\text{,} +\end{aligned} +\end{equation*} +where +\begin{equation*} +f(x, p) = \begin{cases} +1 - x, & \text{with probability } p \\ +x, & \text{otherwise.} +\end{cases} +\end{equation*} +At train time $\partial\!\operatorname{dropout}$ randomly negates soft-bit values with probability $p$. At test time, and in the hard-net, $\partial\!\operatorname{dropout}$ is a $\operatorname{nop}$. + +\section{Differentiable counting}\label{sec:counting} + +A boolean counting function $f({\bf x})$ is $\operatorname{True}$ if a counting predicate, $c({\bf x})$, holds over its $n$ inputs. We aim to construct a differentiable analogue of $\operatorname{count}({\bf x}, k)$ where $c({\bf x}) := |\{x_{i} : x_{i} = 1 \}| = k$ (i.e. `exactly $k$ high'), which can be useful in multiclass classification problems. Define +\begin{equation*} +\begin{aligned} +\partial\!\operatorname{count-hot}: [0,1]^{n} &\to [0,1]^{n+1}, \\ +{\bf x} &\mapsto \operatorname{low-high}(\operatorname{sort}({\bf x}))\text{,} +\end{aligned} +\end{equation*} +where +\begin{equation*} +\begin{aligned} +& \operatorname{low-high}: [0,1]^{n} \to [0,1]^{n+1},\\ +& {\bf x} \mapsto \left[ \partial_{\wedge}\!(1, x_{1}), \partial_{\wedge}\!(1 - x_{1}, x_{2}), \dots, +\partial_{\wedge}\!(1 - x_{n-1}, x_{n}), \partial_{\wedge}\!(1-x_{n}, 1) \right]\text{.} +\end{aligned} +\end{equation*} +$\partial\!\operatorname{count-hot}({\bf x})$ outputs a 1-hot vector where the index of the high bit is the number of low bits in ${\bf x}$. Note that $\partial\!\operatorname{count-hot}$ is differentiable, gradient-rich and hard-equivalent to the boolean function +\begin{equation*} +\begin{aligned} +& \operatorname{count-hot}: \{0,1\}^{n} \to \{0,1\}^{n+1}, \\ +{\bf x} &\mapsto \left[\operatorname{k-of-n}({\bf x}, 0), \operatorname{k-of-n}({\bf x}, 1), \dots, \operatorname{k-of-n}({\bf x}, n)\right]\text{,} +\end{aligned} +\end{equation*} +where +\begin{equation*} +\operatorname{k-of-n}({\bf x}, k) = \bigvee_{|S|=k} \bigwedge_{i\in S} x_i \bigwedge_{j\notin S} \neg x_j +\end{equation*} +(see proposition \ref{prop:count}). However, in the hard $\partial\mathbb{B}$ net we efficiently implement $\operatorname{count-hot}$ as a discrete program that simply counts the number of low bits. + +We can construct various kinds of boolean counting functions from $\partial\!\operatorname{count-hot}$. For example, $\partial\!\operatorname{count}({\bf x}, k)$ is straightforwardly $\partial\!\operatorname{count-hot}({\bf x})[k]$ where margin-packing ensures that this single soft-bit is gradient-rich. + +\section{An example of hard-equivalence}\label{sec:discrete} + +\begin{figure}[h!] + \centering + \includegraphics[width=0.49\textwidth]{../toy-example-architecture.png} + \caption{{\em A $\partial\mathbb{B}$ net to illustrate hardening}. The net concatenates a $\partial_{\neg}\!\operatorname{Layer}$ (of width 8) with a reshaping layer that outputs two vectors, which get reduced, by a $\partial\!\operatorname{Maj}$ operator, to 2 soft-bits, one for each class label. A final $\partial\!\operatorname{harden}$ layer ensures the loss is a function of hard bits. The net's weights, once hardened, consume $40$ bits ($5$ bytes).} + \label{fig:toy-example-architecture} +\end{figure} + +The $\partial\mathbb{B}$ net specified in Figure \ref{fig:toy-example-architecture} (with 40 soft-bit weights) has two single-bit output ports and is hard-equivalent to the following discrete program (with 40 hard-bit weights): + +\begin{lstlisting}[language=Python,style=mystyle,frame=single] +def dbNet(very-cold, cold, warm, very-warm, outside): +return [ +ge(sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((0, not(xor(ne(very-cold, 0), w1)))), not(xor(ne(cold, 0), w2)))), not(xor(ne(warm, 0), w3)))), not(xor(ne(very-warm, 0), w4)))), not(xor(ne(outside, 0), w5)))), not(xor(ne(very-cold, 0), w6)))), not(xor(ne(cold, 0), w7)))), not(xor(ne(warm, 0), w8)))), not(xor(ne(very-warm, 0), w9)))), not(xor(ne(outside, 0), w10)))), not(xor(ne(very-cold, 0), w11)))), not(xor(ne(cold, 0), w12)))), not(xor(ne(warm, 0), w13)))), not(xor(ne(very-warm, 0), w14)))), not(xor(ne(outside, 0), w15)))), not(xor(ne(very-cold, 0), w16)))), not(xor(ne(cold, 0), w17)))), not(xor(ne(warm, 0), w18)))), not(xor(ne(very-warm, 0), w19)))), not(xor(ne(outside, 0), w20)))), 11), +ge(sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((0, not(xor(ne(very-cold, 0), w21)))), not(xor(ne(cold, 0), w22)))), not(xor(ne(warm, 0), w23)))), not(xor(ne(very-warm, 0), w24)))), not(xor(ne(outside, 0), w25)))), not(xor(ne(very-cold, 0), w26)))), not(xor(ne(cold, 0), w27)))), not(xor(ne(warm, 0), w28)))), not(xor(ne(very-warm, 0), w29)))), not(xor(ne(outside, 0), w30)))), not(xor(ne(very-cold, 0), w31)))), not(xor(ne(cold, 0), w32)))), not(xor(ne(warm, 0), w33)))), not(xor(ne(very-warm, 0), w34)))), not(xor(ne(outside, 0), w35)))), not(xor(ne(very-cold, 0), w36)))), not(xor(ne(cold, 0), w37)))), not(xor(ne(warm, 0), w38)))), not(xor(ne(very-warm, 0), w39)))), not(xor(ne(outside, 0), w40)))), 11) +] +\end{lstlisting} + +\section{Experiments}\label{sec:experiments} + +The $\partial\mathbb{B}$ net library is implemented in Flax \cite{flax2020github} and JAX \cite{jax2018github} and available at {\small \url{github.com/Z80coder/db-nets}}. The library supports the specification of a $\partial\mathbb{B}$ net as Python code, which automatically defines (i) the soft-net for training (weights are floats), (ii) a hard-net for inference (weights are booleans), and (iii) a symbolic net for interpretation (weights and inputs are symbols). The symbolic net, when evaluated, interprets its own JAX expression and outputs a description of the discrete program it computes. + +We compare the performance of $\partial\mathbb{B}$ nets against standard ML approaches on three problems: the classic Iris dataset, an adversarial noisy XOR problem, and MNIST. + +\subsection{Binary Iris} + +\begin{figure} + \centering + \includegraphics[width=0.75\textwidth]{../binary-iris-architecture.png} + \caption{{\em A $\partial\mathbb{B}$ net for the binary Iris problem}. The net concatenates the soft-bit input, ${\bf x}$ (length 16), with its negation, ${\bf 1 - x}$, and supplies the resulting vector (length 32) to a $\partial_{\wedge}\!\operatorname{Layer}$ (width 59), a $\partial\!\operatorname{dropout}$ layer for improved generalisation, a $\partial\!\operatorname{count-hot}$ layer that generates a 1-hot vector (width 60) that is reduced by $\operatorname{max}$ to a 1-hot vector of 3 classification bits. A final $\partial\!\operatorname{harden}$ ensures the loss is a function of hard bits. The net's weights, once hardened, consume $236$ bytes.} + \label{fig:binary-iris-architecture} +\end{figure} + + +The Iris dataset has 150 examples with 4 inputs (sepal length and width, and petal length and width), and 3 labels ({\em setosa}, {\em versicolour}, and {\em virginica}). We use the binary version of the Iris dataset \cite{binary-iris-dataset} where each input float is represented by 4 bits. We perform 1000 experiments, each with a different random seed. Each experiment randomly partitions the data into 80\% training and 20\% test sets. We initialize the network, described in Figure \ref{fig:binary-iris-architecture}, with all weights $w_{i} = 0.3$ and train for 1000 epochs with the RAdam optimizer and softmax cross-entropy loss. + +We measure the accuracy of the final net to avoid hand-picking the best configuration. Table \ref{tab:binary-iris-results} compares the $\delta\mathbb{B}$ net against other classifiers \cite{granmo18}. Naive Bayes performs the worst. The Tsetlin machine performs best on this problem, with the $\partial\mathbb{B}$ net second. + +\begin{table}[t] + \centering + \begin{tabular}{llllll} + \cline{2-6} + \multicolumn{1}{c}{} & \multicolumn{5}{c}{\textbf{accuracy}} \\ \cline{2-6} + \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{mean} & \multicolumn{1}{l|}{5 \%ile} & \multicolumn{1}{l|}{95 \%ile} & \multicolumn{1}{l|}{min} & \multicolumn{1}{l|}{max} \\ \hline + \multicolumn{1}{|l|}{Tsetlin} & \multicolumn{1}{l|}{95.0 +/- 0.2} & \multicolumn{1}{l|}{86.7} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{80.0} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{$\partial\mathbb{B}$} & \multicolumn{1}{l|}{\textbf{93.9 +/- 0.1}} & \multicolumn{1}{l|}{\textbf{86.7}} & \multicolumn{1}{l|}{\textbf{100.0}} & \multicolumn{1}{l|}{\textbf{80.0}} & \multicolumn{1}{l|}{\textbf{100.0}} \\ \hline + \multicolumn{1}{|l|}{neural network} & \multicolumn{1}{l|}{93.8 +/- 0.2} & \multicolumn{1}{l|}{86.7} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{80.0} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{SVM} & \multicolumn{1}{l|}{93.6 +/- 0.3} & \multicolumn{1}{l|}{86.7} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{76.7} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{naive Bayes} & \multicolumn{1}{l|}{91.6 +/- 0.3} & \multicolumn{1}{l|}{83.3} & \multicolumn{1}{l|}{96.7} & \multicolumn{1}{l|}{70.0} & \multicolumn{1}{l|}{100.0} \\ \hline + \end{tabular} + \caption{{\em Binary Iris results} measured over 1000 experiments.} + \label{tab:binary-iris-results} +\end{table} + +\subsection{Noisy XOR} + +\begin{figure} + \centering + \includegraphics[width=0.75\textwidth]{../noisy-xor-architecture.png} + \caption{{\em A $\partial\mathbb{B}$ net for the noisy xor problem}. The net concatenates the soft-bit input, ${\bf x}$ (length 12), with its negation, ${\bf 1 - x}$, and supplies the resulting vector (length 24) to a $\partial_{\wedge}\!\!\operatorname{Layer}$ (width 32), $\partial_{\vee}\!\!\operatorname{Layer}$ (width 32), $\partial_{\neg} \!\operatorname{Layer}$ (width 16), and a final $\partial\!\operatorname{Maj}$ to produce a single soft-bit $y \in [0,1]$ (to predict odd parity) and its negation $1-y$ (to predict even parity). The net's weights, once hardened, consume $288$ bytes.} + \label{fig:noisy-xor-architecture} +\end{figure} + +The noisy XOR dataset \cite{noisy-xor-dataset} is an adversarial parity problem with noisy non-informative features. The dataset consists of 10K examples with 12 boolean inputs and a target label (where 0 = odd and 1 = even) that is a XOR function of 2 of the inputs. The remaining 10 inputs are entirely random. We train on 50\% of the data where, additionally, 40\% of the labels are inverted. We initialize the network described in Figure \ref{fig:noisy-xor-architecture} with random weights distributed close to the hard threshold at $1/2$ (i.e. in the $\partial_{\wedge}\!\operatorname{Layer}$, $w_{i} = 0.501 \times b + 0.3 \times (1-b)$ where $b \sim \operatorname{Bernoulli}(0.01)$; in the $\partial_{\vee}\!\operatorname{Layer}$, $w_{i} = 0.7 \times b + 0.499 \times (1-b)$ where $b \sim \operatorname{Bernoulli}(0.99)$); and in the $\partial_{\neg}\!\operatorname{Layer}$, $w_{i} \sim \operatorname{Uniform}(0.499, 0.501)$. We train for 2000 epochs with the RAdam optimizer and softmax cross-entropy loss. + +We measure the accuracy of the final net on the test data to avoid hand-picking the best configuration. Table \ref{tab:noisy-xor-results} compares the $\partial\mathbb{B}$ net against other classifiers \cite{granmo18}. The high noise causes logistic regression and naive Bayes to randomly guess. The SVM hardly performs better. In contrast, the multilayer neural network, Tsetlin machine, and $\partial\mathbb{B}$ net all successfully learn the underlying XOR signal. The Tsetlin machine performs best on this problem, with the $\partial\mathbb{B}$ net second. + +\begin{table}[t] + \centering + \begin{tabular}{llllll} + \cline{2-6} + \multicolumn{1}{c}{} & \multicolumn{5}{c}{\textbf{accuracy}} \\ \cline{2-6} + \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{mean} & \multicolumn{1}{l|}{5 \%ile} & \multicolumn{1}{l|}{95 \%ile} & \multicolumn{1}{l|}{min} & \multicolumn{1}{l|}{max} \\ \hline + \multicolumn{1}{|l|}{Tsetlin} & \multicolumn{1}{l|}{99.3 +/- 0.3} & \multicolumn{1}{l|}{95.9} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{91.6} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{$\partial\mathbb{B}$} & \multicolumn{1}{l|}{\textbf{97.9 +/- 0.2}} & \multicolumn{1}{l|}{\textbf{95.4}} & \multicolumn{1}{l|}{\textbf{100.0}} & \multicolumn{1}{l|}{\textbf{93.6}} & \multicolumn{1}{l|}{\textbf{100.0}} \\ \hline + \multicolumn{1}{|l|}{neural network} & \multicolumn{1}{l|}{95.4 +/- 0.5} & \multicolumn{1}{l|}{90.1} & \multicolumn{1}{l|}{98.6} & \multicolumn{1}{l|}{88.2} & \multicolumn{1}{l|}{99.9} \\ \hline + \multicolumn{1}{|l|}{SVM} & \multicolumn{1}{l|}{58.0 +/- 0.3} & \multicolumn{1}{l|}{56.4} & \multicolumn{1}{l|}{59.2} & \multicolumn{1}{l|}{55.4} & \multicolumn{1}{l|}{66.5} \\ \hline + \multicolumn{1}{|l|}{naive Bayes} & \multicolumn{1}{l|}{49.8 +/- 0.2} & \multicolumn{1}{l|}{48.3} & \multicolumn{1}{l|}{51.0} & \multicolumn{1}{l|}{41.3} & \multicolumn{1}{l|}{52.7} \\ \hline + \multicolumn{1}{|l|}{logistic regression} & \multicolumn{1}{l|}{49.8 +/- 0.3} & \multicolumn{1}{l|}{47.8} & \multicolumn{1}{l|}{51.1} & \multicolumn{1}{l|}{41.1} & \multicolumn{1}{l|}{53.1} \\ \hline + \end{tabular} + \caption{{\em Noisy XOR results} measured over 100 experiments.} + \label{tab:noisy-xor-results} +\end{table} + +\subsection{MNIST} + +\begin{figure} + \centering + \includegraphics[width=0.75\textwidth]{../mnist-architecture.png} + \caption{{\em A non-convolutional $\partial\mathbb{B}$ net for MNIST}. The input is a $28\times28$ bit matrix representing an image. The net consists of a $\partial_{\Rightarrow}\!\operatorname{Layer}$ (of width 60, to produce a $2940\times16$ reshaped array), a $\partial\!\operatorname{Maj}$ layer (to produce a vector of size $2940$), a $\partial_{\neg}\!\operatorname{Layer}$ (of width 20, to produce a $20 \times 2940$ array), and a final $\partial\!\operatorname{harden}$ operator to generate hard-bits split into 10 buckets and summed to produce 10 integer logits. The net's weights, once hardened, consume 13.23 kb.} + \label{fig:mnist-architecture} +\end{figure} + + +\begin{table}[t] + \centering + \begin{tabular}{lc} + \cline{2-2} + & \textbf{accuracy} \\ \hline + \multicolumn{1}{|l|}{\em 2-layer NN, 800 HU, cross-entropy loss} & \multicolumn{1}{c|}{98.6} \\ \hline + \multicolumn{1}{|l|}{Tsetlin} & \multicolumn{1}{c|}{98.2 +/- 0.0} \\ \hline + \multicolumn{1}{|l|}{\em K-nearest-neighbours, L3} & \multicolumn{1}{c|}{97.2} \\ \hline + \multicolumn{1}{|l|}{$\partial\mathbb{B}$} & \multicolumn{1}{c|}{\textbf{94.0}} \\ \hline + \multicolumn{1}{|l|}{Logistic regression} & \multicolumn{1}{c|}{91.5} \\ \hline + \multicolumn{1}{|l|}{\em Linear classifier (1-layer NN)} & \multicolumn{1}{c|}{88.0} \\ \hline + \multicolumn{1}{|l|}{Decision tree} & \multicolumn{1}{c|}{87.8} \\ \hline + \multicolumn{1}{|l|}{Multinomial Naive Bayes} & \multicolumn{1}{c|}{83.2} \\ \hline + \end{tabular} + \caption{{\em MNIST results}. A classifier in {\em italics} was trained on grey-value pixel data, otherwise the classifier was trained on binarized data. Note: the $\partial\mathbb{B}$ results are from a small model that under-fits the data (due to OOM errors on my GPU). The next draft will include results using a larger $\partial\mathbb{B}$ net.} + \label{tab:mnist-table} +\end{table} + +The MNIST dataset \cite{726791} consists of 60K training and 10K test examples of handwritten digits (0-9). We binarize the data by replacing pixels with grey value greater than 0.3 with 1, otherwise with 0. We initialize the network described in Figure \ref{fig:mnist-architecture} with random weights distributed as $w_{i} = 0.501 \times b + 0.3 \times (1-b)$ where $b \sim \operatorname{Bernoulli}(0.01)$. We train for 1000 epochs with a batch size of 6000 using the RAdam optimizer and softmax cross-entropy loss. + +We measure the accuracy on the final net. Table \ref{tab:mnist-table} compares the $\partial\mathbb{B}$ net against other classifiers (reference data taken from \citemyauthoryear{granmo18}). Basic versions of the algorithms (e.g. no convolutional nets) are applied to unenhanced data (e.g. no data augmentation). The aim is to compare raw performance rather than optimise for MNIST. A 2-layer neural network trained on grey-value pixel data performs best. A Tsetlin machine of 40,000 automata each with 256 states (and therefore 40 kb of parameters) trained on binary data achieves $\approx 98.2\%$ accuracy. A $\partial\mathbb{B}$ net with 105,840 soft-bit weights that harden to 1-bit booleans (and therefore 13.23 kb of parameters) trained on binary data achieves $\approx 94.0\%$ accuracy. However, this $\partial\mathbb{B}$ net underfits the training data and we expect better performance from a larger model. + +\section{Proofs} + +\begin{proposition}\label{prop:not} + $\partial_{\neg}(x,y) \btright \neg (x \oplus y)$. + \begin{proof} + Table \ref{not-table} is the truth table of the boolean function $\neg (x \oplus w)$, where $h(x) = \operatorname{harden}(x)$. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\neg}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\neg}(x, y))$} + &\multicolumn{1}{c}{$\neg (h(y) \oplus h(x))$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2}, 1\right]$ & 1 & 1\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\neg}(x,y) \btright \neg (y \oplus x)$.}\label{not-table} + \end{table} + \end{proof} +\end{proposition} + +\begin{lemma}\label{prop:augmented} + If a representative bit, $x_{i}$, is hard-equivalent to a target function, $g$, then so is the augmented bit, $z$. + \begin{proof} + As $x_{i}$ is representative then $\operatorname{harden}(x_{i}) = g(\operatorname{harden}({\bf x}))$. The augmented bit, $z$, is given by \eqref{eq:augmented-bit}: + \begin{equation*} + z = \begin{cases} + 1/2 + \bar{\bf x}\times|x_{i} - 1/2| & \text{if } x_{i} > 1/2 \\ + x_{i} + \bar{\bf x}\times|x_{i} - 1/2| & \text{otherwise.} + \end{cases} + \end{equation*} + In consequence, + \begin{equation*} + \operatorname{harden}(z) = \begin{cases} + 1 & \text{if } x > 1/2 \\ + 0 & \text{otherwise,} + \end{cases} + \end{equation*} + since $x_{i} > 1/2 \Rightarrow z > 1/2$ and $x_{i} \leq 1/2 \Rightarrow z \leq 1/2$. Hence, $\operatorname{harden}(z) = \operatorname{harden}(x_{i}) = g(\operatorname{harden}({\bf x}))$ + \end{proof} +\end{lemma} + + +\begin{proposition}\label{prop:and} + $\partial_{\wedge}\!(x,y) \btright x \wedge y$. + \begin{proof} + Table \ref{and-table} is the truth table of the boolean function $x \wedge y$, where $h(x) = \operatorname{harden}(x)$.. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\wedge}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\wedge}(x, y))$} + &\multicolumn{1}{c}{$h(x) \wedge h(y)$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left(\frac{1}{4}, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left(\frac{1}{4}, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2}, 1\right]$ & 1 & 1\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\wedge}(x,y) \btright x \wedge y$.}\label{and-table} + \end{table} + \end{proof} +\end{proposition} + +\begin{proposition}\label{prop:or} + $\partial_{\vee}\!(x,y) \btright x \vee y$. + \begin{proof} + Table \ref{or-table} is the truth table of the boolean function $x \vee y$, where $h(x) = \operatorname{harden}(x)$.. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\vee}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\vee}(x, y))$} + &\multicolumn{1}{c}{$h(x) \vee h(y)$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left[0,\frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\vee}(x,y) \btright x \vee y$.}\label{or-table} + \end{table} + \end{proof} +\end{proposition} + +\begin{proposition}\label{prop:implies} + $\partial_{\Rightarrow}\!(x,y) \btright x \Rightarrow y$. + \begin{proof} + Table \ref{implies-table} is the truth table of the boolean function $x \Rightarrow y$, where $h(x) = \operatorname{harden}(x)$.. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\Rightarrow}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\Rightarrow}(x, y))$} + &\multicolumn{1}{c}{$h(x) \Rightarrow h(y)$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left(\frac{1}{2}, 1\right]$ & 1 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left(\frac{1}{2},1\right]$ & 1 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2}, \frac{7}{8}\right)$ & 1 & 0\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\Rightarrow}(x,y) \btright x \Rightarrow y$.}\label{implies-table} + \end{table} + \end{proof} +\end{proposition} + +\begin{lemma} + \label{lem:maj} + Let $i$ = $\operatorname{majority-index}({\bf x})$, then the $i$th element of $\operatorname{sort}({\bf x})$ is hard-equivalent to boolean majority, i.e. $\operatorname{harden}(\operatorname{sort}({\bf x})[i]) = \operatorname{Maj}(\operatorname{harden}({\bf x}))$. + \begin{proof} + Let $h$ denote the number of bits that are high in ${\bf x} = [x_{1}, \dots, x_{n}]$. Then indices $\{j : n-h+1 \leq j \leq n\}$ are high in $\operatorname{sort}({\bf x})$. If the majority of bits are high, $h \geq \lfloor n/2 + 1 \rfloor$, then index $j=n - \lfloor n/2 + 1 \rfloor + 1 = n - \lfloor n/2 \rfloor = \lceil n/2 \rceil$ is high in $\operatorname{sort}({\bf x})$. $\operatorname{majority-index}$ selects index $i = \lceil n/2 \rceil$ and therefore $i=j$. Hence, if the majority of bits are high then $\operatorname{sort}({\bf x})[i]$ is high. Similarly, if the majority of bits are low, $h < \lfloor n/2 + 1 \rfloor$, then index $j=n - \lfloor n/2 + 1 \rfloor + 1 = n - \lfloor n/2 \rfloor = \lceil n/2 \rceil$ is low in $\operatorname{sort}({\bf x})$. Hence, if the majority of bits are low then $\operatorname{sort}({\bf x})[i]$ is low. + + Note that $h \geq \lfloor n/2 + 1 \rfloor$ implies that $\operatorname{Maj}(\operatorname{harden}({\bf x})) \geq \left\lfloor \frac{1}{2} + \frac{1}{n}\left(\frac{n}{2} + 1 - \frac{1}{2} \right) \right\rfloor \geq \left\lfloor 1 + \frac{1}{2n} \right\rfloor = 1$, and $h < \lfloor n/2 + 1 \rfloor$ implies that $\operatorname{Maj}(\operatorname{harden}({\bf x})) < \left\lfloor 1 + \frac{1}{2n} \right\rfloor = 0$. + + In consequence, $\operatorname{harden}(\operatorname{sort}({\bf x})[i]) = \operatorname{Maj}(\operatorname{harden}({\bf x}))$ for all $h \in [0,\dots, n]$. + \end{proof} +\end{lemma} + +\begin{theorem}\label{prop:majority} + $\partial\!\operatorname{Maj} \btright \operatorname{Maj}$. + \begin{proof} + $\partial\!\operatorname{Maj}$ augments the representative bit $x_{i} = \operatorname{sort}({\bf x})[\operatorname{majority-index}({\bf x})]$. By lemma \ref{lem:maj} the representative bit is $\btright \operatorname{Maj}(\operatorname{harden}({\bf x}))$. + By lemma \ref{prop:augmented}, the augmented bit, $\operatorname{augmented-bit}(\operatorname{sort}({\bf x}), \operatorname{majority-index}({\bf x}))$, is also $\btright\!\operatorname{Maj}(\operatorname{harden}({\bf x}))$. Hence $\partial\!\operatorname{Maj} \btright\!\operatorname{Maj}$. + \end{proof} +\end{theorem} + +\begin{proposition}\label{prop:count} + $\partial\!\operatorname{count-hot} \btright \operatorname{count-hot}$. + \begin{proof} + Let $l$ denote the number of bits that are low in ${\bf x} = [x_{1},\dots,x_{n}]$, and let ${\bf y} = \partial\!\operatorname{count-hot}({\bf x})$. Then ${\bf y}[l+1]$ is high and any ${\bf y}[i]$, where $i \neq l+1$, is low. Let ${\bf z} = \operatorname{count-hot}(\operatorname{harden}({\bf x}))$. Then ${\bf z}[l+1]$ is high and any ${\bf z}[i]$, where $i \neq l+1$, is low. Hence, $\operatorname{harden}({\bf y}) = {\bf z}$, and therefore $\partial\!\operatorname{count-hot} \btright \operatorname{count-hot}$. + \end{proof} +\end{proposition} + + +\end{document} + +\begin{comment} +Define +\begin{equation*} +\begin{aligned} +\partial\text{AND-LAYER}: [0,1]^{n \times m} \times [0,1]^{m} &\to [0,1]^{n}, \\ +({\bf W}, {\bf x}) &\mapsto [\partial_{\wedge}\operatorname{Neuron}({\bf W}_{1}, {\bf x}), \dots, \partial_{\wedge}\operatorname{Neuron}({\bf W}_{n}, {\bf x})] +\end{aligned} +\end{equation*} +\end{comment} + + +\end{document} + + +% This document was modified from the file originally made available by +% Pat Langley and Andrea Danyluk for ICML-2K. This version was created +% by Iain Murray in 2018, and modified by Alexandre Bouchard in +% 2019 and 2021 and by Csaba Szepesvari, Gang Niu and Sivan Sabato in 2022. +% Modified again in 2023 by Sivan Sabato and Jonathan Scarlett. +% Previous contributors include Dan Roy, Lise Getoor and Tobias +% Scheffer, which was slightly modified from the 2010 version by +% Thorsten Joachims & Johannes Fuernkranz, slightly modified from the +% 2009 version by Kiri Wagstaff and Sam Roweis's 2008 version, which is +% slightly modified from Prasad Tadepalli's 2007 version which is a +% lightly changed version of the previous year's version by Andrew +% Moore, which was in turn edited from those of Kristian Kersting and +% Codrina Lauth. Alex Smola contributed to the algorithmic style files. diff --git a/docs/ICML_workshop/icml2023-diffxyz/algorithm.sty b/docs/ICML_workshop/icml2023-diffxyz/algorithm.sty new file mode 100644 index 0000000..a723c1c --- /dev/null +++ b/docs/ICML_workshop/icml2023-diffxyz/algorithm.sty @@ -0,0 +1,79 @@ +% ALGORITHM STYLE -- Released 8 April 1996 +% for LaTeX-2e +% Copyright -- 1994 Peter Williams +% E-mail Peter.Williams@dsto.defence.gov.au +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithm} +\typeout{Document Style `algorithm' - floating environment} + +\RequirePackage{float} +\RequirePackage{ifthen} +\newcommand{\ALG@within}{nothing} +\newboolean{ALG@within} +\setboolean{ALG@within}{false} +\newcommand{\ALG@floatstyle}{ruled} +\newcommand{\ALG@name}{Algorithm} +\newcommand{\listalgorithmname}{List of \ALG@name s} + +% Declare Options +% first appearance +\DeclareOption{plain}{ + \renewcommand{\ALG@floatstyle}{plain} +} +\DeclareOption{ruled}{ + \renewcommand{\ALG@floatstyle}{ruled} +} +\DeclareOption{boxed}{ + \renewcommand{\ALG@floatstyle}{boxed} +} +% then numbering convention +\DeclareOption{part}{ + \renewcommand{\ALG@within}{part} + \setboolean{ALG@within}{true} +} +\DeclareOption{chapter}{ + \renewcommand{\ALG@within}{chapter} + \setboolean{ALG@within}{true} +} +\DeclareOption{section}{ + \renewcommand{\ALG@within}{section} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsection}{ + \renewcommand{\ALG@within}{subsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsubsection}{ + \renewcommand{\ALG@within}{subsubsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{nothing}{ + \renewcommand{\ALG@within}{nothing} + \setboolean{ALG@within}{true} +} +\DeclareOption*{\edef\ALG@name{\CurrentOption}} + +% ALGORITHM +% +\ProcessOptions +\floatstyle{\ALG@floatstyle} +\ifthenelse{\boolean{ALG@within}}{ + \ifthenelse{\equal{\ALG@within}{part}} + {\newfloat{algorithm}{htbp}{loa}[part]}{} + \ifthenelse{\equal{\ALG@within}{chapter}} + {\newfloat{algorithm}{htbp}{loa}[chapter]}{} + \ifthenelse{\equal{\ALG@within}{section}} + {\newfloat{algorithm}{htbp}{loa}[section]}{} + \ifthenelse{\equal{\ALG@within}{subsection}} + {\newfloat{algorithm}{htbp}{loa}[subsection]}{} + \ifthenelse{\equal{\ALG@within}{subsubsection}} + {\newfloat{algorithm}{htbp}{loa}[subsubsection]}{} + \ifthenelse{\equal{\ALG@within}{nothing}} + {\newfloat{algorithm}{htbp}{loa}}{} +}{ + \newfloat{algorithm}{htbp}{loa} +} +\floatname{algorithm}{\ALG@name} + +\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}} + diff --git a/docs/ICML_workshop/icml2023-diffxyz/fancyhdr.sty b/docs/ICML_workshop/icml2023-diffxyz/fancyhdr.sty new file mode 100644 index 0000000..5a4d897 --- /dev/null +++ b/docs/ICML_workshop/icml2023-diffxyz/fancyhdr.sty @@ -0,0 +1,485 @@ +% fancyhdr.sty version 3.2 +% Fancy headers and footers for LaTeX. +% Piet van Oostrum, +% Dept of Computer and Information Sciences, University of Utrecht, +% Padualaan 14, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands +% Telephone: +31 30 2532180. Email: piet@cs.uu.nl +% ======================================================================== +% LICENCE: +% This file may be distributed under the terms of the LaTeX Project Public +% License, as described in lppl.txt in the base LaTeX distribution. +% Either version 1 or, at your option, any later version. +% ======================================================================== +% MODIFICATION HISTORY: +% Sep 16, 1994 +% version 1.4: Correction for use with \reversemargin +% Sep 29, 1994: +% version 1.5: Added the \iftopfloat, \ifbotfloat and \iffloatpage commands +% Oct 4, 1994: +% version 1.6: Reset single spacing in headers/footers for use with +% setspace.sty or doublespace.sty +% Oct 4, 1994: +% version 1.7: changed \let\@mkboth\markboth to +% \def\@mkboth{\protect\markboth} to make it more robust +% Dec 5, 1994: +% version 1.8: corrections for amsbook/amsart: define \@chapapp and (more +% importantly) use the \chapter/sectionmark definitions from ps@headings if +% they exist (which should be true for all standard classes). +% May 31, 1995: +% version 1.9: The proposed \renewcommand{\headrulewidth}{\iffloatpage... +% construction in the doc did not work properly with the fancyplain style. +% June 1, 1995: +% version 1.91: The definition of \@mkboth wasn't restored on subsequent +% \pagestyle{fancy}'s. +% June 1, 1995: +% version 1.92: The sequence \pagestyle{fancyplain} \pagestyle{plain} +% \pagestyle{fancy} would erroneously select the plain version. +% June 1, 1995: +% version 1.93: \fancypagestyle command added. +% Dec 11, 1995: +% version 1.94: suggested by Conrad Hughes +% CJCH, Dec 11, 1995: added \footruleskip to allow control over footrule +% position (old hardcoded value of .3\normalbaselineskip is far too high +% when used with very small footer fonts). +% Jan 31, 1996: +% version 1.95: call \@normalsize in the reset code if that is defined, +% otherwise \normalsize. +% this is to solve a problem with ucthesis.cls, as this doesn't +% define \@currsize. Unfortunately for latex209 calling \normalsize doesn't +% work as this is optimized to do very little, so there \@normalsize should +% be called. Hopefully this code works for all versions of LaTeX known to +% mankind. +% April 25, 1996: +% version 1.96: initialize \headwidth to a magic (negative) value to catch +% most common cases that people change it before calling \pagestyle{fancy}. +% Note it can't be initialized when reading in this file, because +% \textwidth could be changed afterwards. This is quite probable. +% We also switch to \MakeUppercase rather than \uppercase and introduce a +% \nouppercase command for use in headers. and footers. +% May 3, 1996: +% version 1.97: Two changes: +% 1. Undo the change in version 1.8 (using the pagestyle{headings} defaults +% for the chapter and section marks. The current version of amsbook and +% amsart classes don't seem to need them anymore. Moreover the standard +% latex classes don't use \markboth if twoside isn't selected, and this is +% confusing as \leftmark doesn't work as expected. +% 2. include a call to \ps@empty in ps@@fancy. This is to solve a problem +% in the amsbook and amsart classes, that make global changes to \topskip, +% which are reset in \ps@empty. Hopefully this doesn't break other things. +% May 7, 1996: +% version 1.98: +% Added % after the line \def\nouppercase +% May 7, 1996: +% version 1.99: This is the alpha version of fancyhdr 2.0 +% Introduced the new commands \fancyhead, \fancyfoot, and \fancyhf. +% Changed \headrulewidth, \footrulewidth, \footruleskip to +% macros rather than length parameters, In this way they can be +% conditionalized and they don't consume length registers. There is no need +% to have them as length registers unless you want to do calculations with +% them, which is unlikely. Note that this may make some uses of them +% incompatible (i.e. if you have a file that uses \setlength or \xxxx=) +% May 10, 1996: +% version 1.99a: +% Added a few more % signs +% May 10, 1996: +% version 1.99b: +% Changed the syntax of \f@nfor to be resistent to catcode changes of := +% Removed the [1] from the defs of \lhead etc. because the parameter is +% consumed by the \@[xy]lhead etc. macros. +% June 24, 1997: +% version 1.99c: +% corrected \nouppercase to also include the protected form of \MakeUppercase +% \global added to manipulation of \headwidth. +% \iffootnote command added. +% Some comments added about \@fancyhead and \@fancyfoot. +% Aug 24, 1998 +% version 1.99d +% Changed the default \ps@empty to \ps@@empty in order to allow +% \fancypagestyle{empty} redefinition. +% Oct 11, 2000 +% version 2.0 +% Added LPPL license clause. +% +% A check for \headheight is added. An errormessage is given (once) if the +% header is too large. Empty headers don't generate the error even if +% \headheight is very small or even 0pt. +% Warning added for the use of 'E' option when twoside option is not used. +% In this case the 'E' fields will never be used. +% +% Mar 10, 2002 +% version 2.1beta +% New command: \fancyhfoffset[place]{length} +% defines offsets to be applied to the header/footer to let it stick into +% the margins (if length > 0). +% place is like in fancyhead, except that only E,O,L,R can be used. +% This replaces the old calculation based on \headwidth and the marginpar +% area. +% \headwidth will be dynamically calculated in the headers/footers when +% this is used. +% +% Mar 26, 2002 +% version 2.1beta2 +% \fancyhfoffset now also takes h,f as possible letters in the argument to +% allow the header and footer widths to be different. +% New commands \fancyheadoffset and \fancyfootoffset added comparable to +% \fancyhead and \fancyfoot. +% Errormessages and warnings have been made more informative. +% +% Dec 9, 2002 +% version 2.1 +% The defaults for \footrulewidth, \plainheadrulewidth and +% \plainfootrulewidth are changed from \z@skip to 0pt. In this way when +% someone inadvertantly uses \setlength to change any of these, the value +% of \z@skip will not be changed, rather an errormessage will be given. + +% March 3, 2004 +% Release of version 3.0 + +% Oct 7, 2004 +% version 3.1 +% Added '\endlinechar=13' to \fancy@reset to prevent problems with +% includegraphics in header when verbatiminput is active. + +% March 22, 2005 +% version 3.2 +% reset \everypar (the real one) in \fancy@reset because spanish.ldf does +% strange things with \everypar between << and >>. + +\def\ifancy@mpty#1{\def\temp@a{#1}\ifx\temp@a\@empty} + +\def\fancy@def#1#2{\ifancy@mpty{#2}\fancy@gbl\def#1{\leavevmode}\else + \fancy@gbl\def#1{#2\strut}\fi} + +\let\fancy@gbl\global + +\def\@fancyerrmsg#1{% + \ifx\PackageError\undefined + \errmessage{#1}\else + \PackageError{Fancyhdr}{#1}{}\fi} +\def\@fancywarning#1{% + \ifx\PackageWarning\undefined + \errmessage{#1}\else + \PackageWarning{Fancyhdr}{#1}{}\fi} + +% Usage: \@forc \var{charstring}{command to be executed for each char} +% This is similar to LaTeX's \@tfor, but expands the charstring. + +\def\@forc#1#2#3{\expandafter\f@rc\expandafter#1\expandafter{#2}{#3}} +\def\f@rc#1#2#3{\def\temp@ty{#2}\ifx\@empty\temp@ty\else + \f@@rc#1#2\f@@rc{#3}\fi} +\def\f@@rc#1#2#3\f@@rc#4{\def#1{#2}#4\f@rc#1{#3}{#4}} + +% Usage: \f@nfor\name:=list\do{body} +% Like LaTeX's \@for but an empty list is treated as a list with an empty +% element + +\newcommand{\f@nfor}[3]{\edef\@fortmp{#2}% + \expandafter\@forloop#2,\@nil,\@nil\@@#1{#3}} + +% Usage: \def@ult \cs{defaults}{argument} +% sets \cs to the characters from defaults appearing in argument +% or defaults if it would be empty. All characters are lowercased. + +\newcommand\def@ult[3]{% + \edef\temp@a{\lowercase{\edef\noexpand\temp@a{#3}}}\temp@a + \def#1{}% + \@forc\tmpf@ra{#2}% + {\expandafter\if@in\tmpf@ra\temp@a{\edef#1{#1\tmpf@ra}}{}}% + \ifx\@empty#1\def#1{#2}\fi} +% +% \if@in +% +\newcommand{\if@in}[4]{% + \edef\temp@a{#2}\def\temp@b##1#1##2\temp@b{\def\temp@b{##1}}% + \expandafter\temp@b#2#1\temp@b\ifx\temp@a\temp@b #4\else #3\fi} + +\newcommand{\fancyhead}{\@ifnextchar[{\f@ncyhf\fancyhead h}% + {\f@ncyhf\fancyhead h[]}} +\newcommand{\fancyfoot}{\@ifnextchar[{\f@ncyhf\fancyfoot f}% + {\f@ncyhf\fancyfoot f[]}} +\newcommand{\fancyhf}{\@ifnextchar[{\f@ncyhf\fancyhf{}}% + {\f@ncyhf\fancyhf{}[]}} + +% New commands for offsets added + +\newcommand{\fancyheadoffset}{\@ifnextchar[{\f@ncyhfoffs\fancyheadoffset h}% + {\f@ncyhfoffs\fancyheadoffset h[]}} +\newcommand{\fancyfootoffset}{\@ifnextchar[{\f@ncyhfoffs\fancyfootoffset f}% + {\f@ncyhfoffs\fancyfootoffset f[]}} +\newcommand{\fancyhfoffset}{\@ifnextchar[{\f@ncyhfoffs\fancyhfoffset{}}% + {\f@ncyhfoffs\fancyhfoffset{}[]}} + +% The header and footer fields are stored in command sequences with +% names of the form: \f@ncy with for [eo], from [lcr] +% and from [hf]. + +\def\f@ncyhf#1#2[#3]#4{% + \def\temp@c{}% + \@forc\tmpf@ra{#3}% + {\expandafter\if@in\tmpf@ra{eolcrhf,EOLCRHF}% + {}{\edef\temp@c{\temp@c\tmpf@ra}}}% + \ifx\@empty\temp@c\else + \@fancyerrmsg{Illegal char `\temp@c' in \string#1 argument: + [#3]}% + \fi + \f@nfor\temp@c{#3}% + {\def@ult\f@@@eo{eo}\temp@c + \if@twoside\else + \if\f@@@eo e\@fancywarning + {\string#1's `E' option without twoside option is useless}\fi\fi + \def@ult\f@@@lcr{lcr}\temp@c + \def@ult\f@@@hf{hf}{#2\temp@c}% + \@forc\f@@eo\f@@@eo + {\@forc\f@@lcr\f@@@lcr + {\@forc\f@@hf\f@@@hf + {\expandafter\fancy@def\csname + f@ncy\f@@eo\f@@lcr\f@@hf\endcsname + {#4}}}}}} + +\def\f@ncyhfoffs#1#2[#3]#4{% + \def\temp@c{}% + \@forc\tmpf@ra{#3}% + {\expandafter\if@in\tmpf@ra{eolrhf,EOLRHF}% + {}{\edef\temp@c{\temp@c\tmpf@ra}}}% + \ifx\@empty\temp@c\else + \@fancyerrmsg{Illegal char `\temp@c' in \string#1 argument: + [#3]}% + \fi + \f@nfor\temp@c{#3}% + {\def@ult\f@@@eo{eo}\temp@c + \if@twoside\else + \if\f@@@eo e\@fancywarning + {\string#1's `E' option without twoside option is useless}\fi\fi + \def@ult\f@@@lcr{lr}\temp@c + \def@ult\f@@@hf{hf}{#2\temp@c}% + \@forc\f@@eo\f@@@eo + {\@forc\f@@lcr\f@@@lcr + {\@forc\f@@hf\f@@@hf + {\expandafter\setlength\csname + f@ncyO@\f@@eo\f@@lcr\f@@hf\endcsname + {#4}}}}}% + \fancy@setoffs} + +% Fancyheadings version 1 commands. These are more or less deprecated, +% but they continue to work. + +\newcommand{\lhead}{\@ifnextchar[{\@xlhead}{\@ylhead}} +\def\@xlhead[#1]#2{\fancy@def\f@ncyelh{#1}\fancy@def\f@ncyolh{#2}} +\def\@ylhead#1{\fancy@def\f@ncyelh{#1}\fancy@def\f@ncyolh{#1}} + +\newcommand{\chead}{\@ifnextchar[{\@xchead}{\@ychead}} +\def\@xchead[#1]#2{\fancy@def\f@ncyech{#1}\fancy@def\f@ncyoch{#2}} +\def\@ychead#1{\fancy@def\f@ncyech{#1}\fancy@def\f@ncyoch{#1}} + +\newcommand{\rhead}{\@ifnextchar[{\@xrhead}{\@yrhead}} +\def\@xrhead[#1]#2{\fancy@def\f@ncyerh{#1}\fancy@def\f@ncyorh{#2}} +\def\@yrhead#1{\fancy@def\f@ncyerh{#1}\fancy@def\f@ncyorh{#1}} + +\newcommand{\lfoot}{\@ifnextchar[{\@xlfoot}{\@ylfoot}} +\def\@xlfoot[#1]#2{\fancy@def\f@ncyelf{#1}\fancy@def\f@ncyolf{#2}} +\def\@ylfoot#1{\fancy@def\f@ncyelf{#1}\fancy@def\f@ncyolf{#1}} + +\newcommand{\cfoot}{\@ifnextchar[{\@xcfoot}{\@ycfoot}} +\def\@xcfoot[#1]#2{\fancy@def\f@ncyecf{#1}\fancy@def\f@ncyocf{#2}} +\def\@ycfoot#1{\fancy@def\f@ncyecf{#1}\fancy@def\f@ncyocf{#1}} + +\newcommand{\rfoot}{\@ifnextchar[{\@xrfoot}{\@yrfoot}} +\def\@xrfoot[#1]#2{\fancy@def\f@ncyerf{#1}\fancy@def\f@ncyorf{#2}} +\def\@yrfoot#1{\fancy@def\f@ncyerf{#1}\fancy@def\f@ncyorf{#1}} + +\newlength{\fancy@headwidth} +\let\headwidth\fancy@headwidth +\newlength{\f@ncyO@elh} +\newlength{\f@ncyO@erh} +\newlength{\f@ncyO@olh} +\newlength{\f@ncyO@orh} +\newlength{\f@ncyO@elf} +\newlength{\f@ncyO@erf} +\newlength{\f@ncyO@olf} +\newlength{\f@ncyO@orf} +\newcommand{\headrulewidth}{0.4pt} +\newcommand{\footrulewidth}{0pt} +\newcommand{\footruleskip}{.3\normalbaselineskip} + +% Fancyplain stuff shouldn't be used anymore (rather +% \fancypagestyle{plain} should be used), but it must be present for +% compatibility reasons. + +\newcommand{\plainheadrulewidth}{0pt} +\newcommand{\plainfootrulewidth}{0pt} +\newif\if@fancyplain \@fancyplainfalse +\def\fancyplain#1#2{\if@fancyplain#1\else#2\fi} + +\headwidth=-123456789sp %magic constant + +% Command to reset various things in the headers: +% a.o. single spacing (taken from setspace.sty) +% and the catcode of ^^M (so that epsf files in the header work if a +% verbatim crosses a page boundary) +% It also defines a \nouppercase command that disables \uppercase and +% \Makeuppercase. It can only be used in the headers and footers. +\let\fnch@everypar\everypar% save real \everypar because of spanish.ldf +\def\fancy@reset{\fnch@everypar{}\restorecr\endlinechar=13 + \def\baselinestretch{1}% + \def\nouppercase##1{{\let\uppercase\relax\let\MakeUppercase\relax + \expandafter\let\csname MakeUppercase \endcsname\relax##1}}% + \ifx\undefined\@newbaseline% NFSS not present; 2.09 or 2e + \ifx\@normalsize\undefined \normalsize % for ucthesis.cls + \else \@normalsize \fi + \else% NFSS (2.09) present + \@newbaseline% + \fi} + +% Initialization of the head and foot text. + +% The default values still contain \fancyplain for compatibility. +\fancyhf{} % clear all +% lefthead empty on ``plain'' pages, \rightmark on even, \leftmark on odd pages +% evenhead empty on ``plain'' pages, \leftmark on even, \rightmark on odd pages +\if@twoside + \fancyhead[el,or]{\fancyplain{}{\sl\rightmark}} + \fancyhead[er,ol]{\fancyplain{}{\sl\leftmark}} +\else + \fancyhead[l]{\fancyplain{}{\sl\rightmark}} + \fancyhead[r]{\fancyplain{}{\sl\leftmark}} +\fi +\fancyfoot[c]{\rm\thepage} % page number + +% Use box 0 as a temp box and dimen 0 as temp dimen. +% This can be done, because this code will always +% be used inside another box, and therefore the changes are local. + +\def\@fancyvbox#1#2{\setbox0\vbox{#2}\ifdim\ht0>#1\@fancywarning + {\string#1 is too small (\the#1): ^^J Make it at least \the\ht0.^^J + We now make it that large for the rest of the document.^^J + This may cause the page layout to be inconsistent, however\@gobble}% + \dimen0=#1\global\setlength{#1}{\ht0}\ht0=\dimen0\fi + \box0} + +% Put together a header or footer given the left, center and +% right text, fillers at left and right and a rule. +% The \lap commands put the text into an hbox of zero size, +% so overlapping text does not generate an errormessage. +% These macros have 5 parameters: +% 1. LEFTSIDE BEARING % This determines at which side the header will stick +% out. When \fancyhfoffset is used this calculates \headwidth, otherwise +% it is \hss or \relax (after expansion). +% 2. \f@ncyolh, \f@ncyelh, \f@ncyolf or \f@ncyelf. This is the left component. +% 3. \f@ncyoch, \f@ncyech, \f@ncyocf or \f@ncyecf. This is the middle comp. +% 4. \f@ncyorh, \f@ncyerh, \f@ncyorf or \f@ncyerf. This is the right component. +% 5. RIGHTSIDE BEARING. This is always \relax or \hss (after expansion). + +\def\@fancyhead#1#2#3#4#5{#1\hbox to\headwidth{\fancy@reset + \@fancyvbox\headheight{\hbox + {\rlap{\parbox[b]{\headwidth}{\raggedright#2}}\hfill + \parbox[b]{\headwidth}{\centering#3}\hfill + \llap{\parbox[b]{\headwidth}{\raggedleft#4}}}\headrule}}#5} + +\def\@fancyfoot#1#2#3#4#5{#1\hbox to\headwidth{\fancy@reset + \@fancyvbox\footskip{\footrule + \hbox{\rlap{\parbox[t]{\headwidth}{\raggedright#2}}\hfill + \parbox[t]{\headwidth}{\centering#3}\hfill + \llap{\parbox[t]{\headwidth}{\raggedleft#4}}}}}#5} + +\def\headrule{{\if@fancyplain\let\headrulewidth\plainheadrulewidth\fi + \hrule\@height\headrulewidth\@width\headwidth \vskip-\headrulewidth}} + +\def\footrule{{\if@fancyplain\let\footrulewidth\plainfootrulewidth\fi + \vskip-\footruleskip\vskip-\footrulewidth + \hrule\@width\headwidth\@height\footrulewidth\vskip\footruleskip}} + +\def\ps@fancy{% +\@ifundefined{@chapapp}{\let\@chapapp\chaptername}{}%for amsbook +% +% Define \MakeUppercase for old LaTeXen. +% Note: we used \def rather than \let, so that \let\uppercase\relax (from +% the version 1 documentation) will still work. +% +\@ifundefined{MakeUppercase}{\def\MakeUppercase{\uppercase}}{}% +\@ifundefined{chapter}{\def\sectionmark##1{\markboth +{\MakeUppercase{\ifnum \c@secnumdepth>\z@ + \thesection\hskip 1em\relax \fi ##1}}{}}% +\def\subsectionmark##1{\markright {\ifnum \c@secnumdepth >\@ne + \thesubsection\hskip 1em\relax \fi ##1}}}% +{\def\chaptermark##1{\markboth {\MakeUppercase{\ifnum \c@secnumdepth>\m@ne + \@chapapp\ \thechapter. \ \fi ##1}}{}}% +\def\sectionmark##1{\markright{\MakeUppercase{\ifnum \c@secnumdepth >\z@ + \thesection. \ \fi ##1}}}}% +%\csname ps@headings\endcsname % use \ps@headings defaults if they exist +\ps@@fancy +\gdef\ps@fancy{\@fancyplainfalse\ps@@fancy}% +% Initialize \headwidth if the user didn't +% +\ifdim\headwidth<0sp +% +% This catches the case that \headwidth hasn't been initialized and the +% case that the user added something to \headwidth in the expectation that +% it was initialized to \textwidth. We compensate this now. This loses if +% the user intended to multiply it by a factor. But that case is more +% likely done by saying something like \headwidth=1.2\textwidth. +% The doc says you have to change \headwidth after the first call to +% \pagestyle{fancy}. This code is just to catch the most common cases were +% that requirement is violated. +% + \global\advance\headwidth123456789sp\global\advance\headwidth\textwidth +\fi} +\def\ps@fancyplain{\ps@fancy \let\ps@plain\ps@plain@fancy} +\def\ps@plain@fancy{\@fancyplaintrue\ps@@fancy} +\let\ps@@empty\ps@empty +\def\ps@@fancy{% +\ps@@empty % This is for amsbook/amsart, which do strange things with \topskip +\def\@mkboth{\protect\markboth}% +\def\@oddhead{\@fancyhead\fancy@Oolh\f@ncyolh\f@ncyoch\f@ncyorh\fancy@Oorh}% +\def\@oddfoot{\@fancyfoot\fancy@Oolf\f@ncyolf\f@ncyocf\f@ncyorf\fancy@Oorf}% +\def\@evenhead{\@fancyhead\fancy@Oelh\f@ncyelh\f@ncyech\f@ncyerh\fancy@Oerh}% +\def\@evenfoot{\@fancyfoot\fancy@Oelf\f@ncyelf\f@ncyecf\f@ncyerf\fancy@Oerf}% +} +% Default definitions for compatibility mode: +% These cause the header/footer to take the defined \headwidth as width +% And to shift in the direction of the marginpar area + +\def\fancy@Oolh{\if@reversemargin\hss\else\relax\fi} +\def\fancy@Oorh{\if@reversemargin\relax\else\hss\fi} +\let\fancy@Oelh\fancy@Oorh +\let\fancy@Oerh\fancy@Oolh + +\let\fancy@Oolf\fancy@Oolh +\let\fancy@Oorf\fancy@Oorh +\let\fancy@Oelf\fancy@Oelh +\let\fancy@Oerf\fancy@Oerh + +% New definitions for the use of \fancyhfoffset +% These calculate the \headwidth from \textwidth and the specified offsets. + +\def\fancy@offsolh{\headwidth=\textwidth\advance\headwidth\f@ncyO@olh + \advance\headwidth\f@ncyO@orh\hskip-\f@ncyO@olh} +\def\fancy@offselh{\headwidth=\textwidth\advance\headwidth\f@ncyO@elh + \advance\headwidth\f@ncyO@erh\hskip-\f@ncyO@elh} + +\def\fancy@offsolf{\headwidth=\textwidth\advance\headwidth\f@ncyO@olf + \advance\headwidth\f@ncyO@orf\hskip-\f@ncyO@olf} +\def\fancy@offself{\headwidth=\textwidth\advance\headwidth\f@ncyO@elf + \advance\headwidth\f@ncyO@erf\hskip-\f@ncyO@elf} + +\def\fancy@setoffs{% +% Just in case \let\headwidth\textwidth was used + \fancy@gbl\let\headwidth\fancy@headwidth + \fancy@gbl\let\fancy@Oolh\fancy@offsolh + \fancy@gbl\let\fancy@Oelh\fancy@offselh + \fancy@gbl\let\fancy@Oorh\hss + \fancy@gbl\let\fancy@Oerh\hss + \fancy@gbl\let\fancy@Oolf\fancy@offsolf + \fancy@gbl\let\fancy@Oelf\fancy@offself + \fancy@gbl\let\fancy@Oorf\hss + \fancy@gbl\let\fancy@Oerf\hss} + +\newif\iffootnote +\let\latex@makecol\@makecol +\def\@makecol{\ifvoid\footins\footnotetrue\else\footnotefalse\fi +\let\topfloat\@toplist\let\botfloat\@botlist\latex@makecol} +\def\iftopfloat#1#2{\ifx\topfloat\empty #2\else #1\fi} +\def\ifbotfloat#1#2{\ifx\botfloat\empty #2\else #1\fi} +\def\iffloatpage#1#2{\if@fcolmade #1\else #2\fi} + +\newcommand{\fancypagestyle}[2]{% + \@namedef{ps@#1}{\let\fancy@gbl\relax#2\relax\ps@fancy}} diff --git a/docs/ICML_workshop/icml2023-diffxyz/icml2023-diffxyz.sty b/docs/ICML_workshop/icml2023-diffxyz/icml2023-diffxyz.sty new file mode 100644 index 0000000..7ccda9e --- /dev/null +++ b/docs/ICML_workshop/icml2023-diffxyz/icml2023-diffxyz.sty @@ -0,0 +1,803 @@ +% File: icml2023.sty (LaTeX style file for ICML-2023, version of 2023-04-25) + +% This file contains the LaTeX formatting parameters for a two-column +% conference proceedings that is 8.5 inches wide by 11 inches high. +% +% Modified by Sivan Sabato 2023: changed years and volume number. +% Modified by Jonathan Scarlett 2023: added page numbers to every page +% +% Modified by Csaba Szepesvari 2022: changed years, PMLR ref. Turned off checking marginparwidth +% as marginparwidth only controls the space available for margin notes and margin notes +% will NEVER be used anyways in submitted versions, so there is no reason one should +% check whether marginparwidth has been tampered with. +% Also removed pdfview=FitH from hypersetup as it did not do its job; the default choice is a bit better +% but of course the double-column format is not supported by this hyperlink preview functionality +% in a completely satisfactory fashion. +% Modified by Gang Niu 2022: Changed color to xcolor +% +% Modified by Iain Murray 2018: changed years, location. Remove affiliation notes when anonymous. +% Move times dependency from .tex to .sty so fewer people delete it. +% +% Modified by Daniel Roy 2017: changed byline to use footnotes for affiliations, and removed emails +% +% Modified by Percy Liang 12/2/2013: changed the year, location from the previous template for ICML 2014 + +% Modified by Fei Sha 9/2/2013: changed the year, location form the previous template for ICML 2013 +% +% Modified by Fei Sha 4/24/2013: (1) remove the extra whitespace after the first author's email address (in %the camera-ready version) (2) change the Proceeding ... of ICML 2010 to 2014 so PDF's metadata will show up % correctly +% +% Modified by Sanjoy Dasgupta, 2013: changed years, location +% +% Modified by Francesco Figari, 2012: changed years, location +% +% Modified by Christoph Sawade and Tobias Scheffer, 2011: added line +% numbers, changed years +% +% Modified by Hal Daume III, 2010: changed years, added hyperlinks +% +% Modified by Kiri Wagstaff, 2009: changed years +% +% Modified by Sam Roweis, 2008: changed years +% +% Modified by Ricardo Silva, 2007: update of the ifpdf verification +% +% Modified by Prasad Tadepalli and Andrew Moore, merely changing years. +% +% Modified by Kristian Kersting, 2005, based on Jennifer Dy's 2004 version +% - running title. If the original title is to long or is breaking a line, +% use \icmltitlerunning{...} in the preamble to supply a shorter form. +% Added fancyhdr package to get a running head. +% - Updated to store the page size because pdflatex does compile the +% page size into the pdf. +% +% Hacked by Terran Lane, 2003: +% - Updated to use LaTeX2e style file conventions (ProvidesPackage, +% etc.) +% - Added an ``appearing in'' block at the base of the first column +% (thus keeping the ``appearing in'' note out of the bottom margin +% where the printer should strip in the page numbers). +% - Added a package option [accepted] that selects between the ``Under +% review'' notice (default, when no option is specified) and the +% ``Appearing in'' notice (for use when the paper has been accepted +% and will appear). +% +% Originally created as: ml2k.sty (LaTeX style file for ICML-2000) +% by P. Langley (12/23/99) + +%%%%%%%%%%%%%%%%%%%% +%% This version of the style file supports both a ``review'' version +%% and a ``final/accepted'' version. The difference is only in the +%% text that appears in the note at the bottom of the first column of +%% the first page. The default behavior is to print a note to the +%% effect that the paper is under review and don't distribute it. The +%% final/accepted version prints an ``Appearing in'' note. To get the +%% latter behavior, in the calling file change the ``usepackage'' line +%% from: +%% \usepackage{icml2023} +%% to +%% \usepackage[accepted]{icml2023} +%%%%%%%%%%%%%%%%%%%% + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{icml2023-diffxyz}[2023/01/03 v2.0 ICML Diff XYZ Conference Style File] + +% Before 2018, \usepackage{times} was in the example TeX, but inevitably +% not everybody did it. +\RequirePackage{times} + +% Use fancyhdr package +\RequirePackage{fancyhdr} +\RequirePackage{xcolor} % changed from color to xcolor (2021/11/24) +\RequirePackage{algorithm} +\RequirePackage{algorithmic} +\RequirePackage{natbib} +\RequirePackage{eso-pic} % used by \AddToShipoutPicture +\RequirePackage{forloop} +\RequirePackage{url} + +%%%%%%%% Options +\DeclareOption{accepted}{% + \renewcommand{\Notice@String}{\ICML@appearing} + \gdef\isaccepted{1} +} + +\DeclareOption{nohyperref}{% + \gdef\nohyperref{1} +} + + + +%%%%%%%%%%%%%%%%%%%% +% This string is printed at the bottom of the page for the +% final/accepted version of the ``appearing in'' note. Modify it to +% change that text. +%%%%%%%%%%%%%%%%%%%% +\newcommand{\ICML@appearing}{\textit{Published at the Differentiable Almost Everything Workshop of the +$\mathit{40}^{th}$ International Conference on Machine Learning}, +Honolulu, Hawaii, USA. July 2023. +Copyright 2023 by the author(s).} + +%%%%%%%%%%%%%%%%%%%% +% This string is printed at the bottom of the page for the draft/under +% review version of the ``appearing in'' note. Modify it to change +% that text. +%%%%%%%%%%%%%%%%%%%% +\newcommand{\Notice@String}{Preliminary work. Under review by the +International Conference on Machine Learning (ICML)\@. Do not distribute.} + +% Cause the declared options to actually be parsed and activated +\ProcessOptions\relax + +\ifdefined\isaccepted\else\ifdefined\hypersetup + \hypersetup{pdfauthor={Anonymous Authors}} + \fi +\fi + +\ifdefined\nohyperref\else\ifdefined\hypersetup + \definecolor{mydarkblue}{rgb}{0,0.08,0.45} + \hypersetup{ % + pdftitle={}, + pdfsubject={Proceedings of the International Conference on Machine Learning 2023}, + pdfkeywords={}, + pdfborder=0 0 0, + pdfpagemode=UseNone, + colorlinks=true, + linkcolor=mydarkblue, + citecolor=mydarkblue, + filecolor=mydarkblue, + urlcolor=mydarkblue, + } + + + \fi +\fi + + + +% Uncomment the following for debugging. It will cause LaTeX to dump +% the version of the ``appearing in'' string that will actually appear +% in the document. +%\typeout{>> Notice string='\Notice@String'} + +% Change citation commands to be more like old ICML styles +\newcommand{\yrcite}[1]{\citeyearpar{#1}} +\renewcommand{\cite}[1]{\citep{#1}} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% to ensure the letter format is used. pdflatex does compile the +% page size into the pdf. This is done using \pdfpagewidth and +% \pdfpageheight. As Latex does not know this directives, we first +% check whether pdflatex or latex is used. +% +% Kristian Kersting 2005 +% +% in order to account for the more recent use of pdfetex as the default +% compiler, I have changed the pdf verification. +% +% Ricardo Silva 2007 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\paperwidth=8.5in +\paperheight=11in + +% old PDFLaTex verification, circa 2005 +% +%\newif\ifpdf\ifx\pdfoutput\undefined +% \pdffalse % we are not running PDFLaTeX +%\else +% \pdfoutput=1 % we are running PDFLaTeX +% \pdftrue +%\fi + +\newif\ifpdf %adapted from ifpdf.sty +\ifx\pdfoutput\undefined +\else + \ifx\pdfoutput\relax + \else + \ifcase\pdfoutput + \else + \pdftrue + \fi + \fi +\fi + +\ifpdf +% \pdfpagewidth=\paperwidth +% \pdfpageheight=\paperheight + \setlength{\pdfpagewidth}{8.5in} + \setlength{\pdfpageheight}{11in} +\fi + +% Physical page layout + +\evensidemargin -0.23in +\oddsidemargin -0.23in +\setlength\textheight{9.0in} +\setlength\textwidth{6.75in} +\setlength\columnsep{0.25in} +\setlength\headheight{10pt} +\setlength\headsep{10pt} +\addtolength{\topmargin}{-20pt} +\addtolength{\topmargin}{-0.29in} + +% Historically many authors tried to include packages like geometry or fullpage, +% which change the page layout. It either makes the proceedings inconsistent, or +% wastes organizers' time chasing authors. So let's nip these problems in the +% bud here. -- Iain Murray 2018. +%\RequirePackage{printlen} +\AtBeginDocument{% +% To get the numbers below, include printlen package above and see lengths like this: +%\printlength\oddsidemargin\\ +%\printlength\headheight\\ +%\printlength\textheight\\ +%\printlength\marginparsep\\ +%\printlength\footskip\\ +%\printlength\hoffset\\ +%\printlength\paperwidth\\ +%\printlength\topmargin\\ +%\printlength\headsep\\ +%\printlength\textwidth\\ +%\printlength\marginparwidth\\ +%\printlength\marginparpush\\ +%\printlength\voffset\\ +%\printlength\paperheight\\ +% +\newif\ifmarginsmessedwith +\marginsmessedwithfalse +\ifdim\oddsidemargin=-16.62178pt \else oddsidemargin has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\headheight=10.0pt \else headheight has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\textheight=650.43pt \else textheight has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\marginparsep=11.0pt \else marginparsep has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\footskip=25.0pt \else footskip has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\hoffset=0.0pt \else hoffset has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\paperwidth=614.295pt \else paperwidth has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\topmargin=-24.95781pt \else topmargin has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\headsep=10.0pt \else headsep has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\textwidth=487.8225pt \else textwidth has been altered.\\ \marginsmessedwithtrue\fi +%\ifdim\marginparwidth=65.0pt \else marginparwidth has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\marginparpush=5.0pt \else marginparpush has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\voffset=0.0pt \else voffset has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\paperheight=794.96999pt \else paperheight has been altered.\\ \marginsmessedwithtrue\fi +\ifmarginsmessedwith + +\textbf{\large \em The page layout violates the ICML style.} + +Please do not change the page layout, or include packages like geometry, +savetrees, or fullpage, which change it for you. + +We're not able to reliably undo arbitrary changes to the style. Please remove +the offending package(s), or layout-changing commands and try again. + +\fi} + + +%% The following is adapted from code in the acmconf.sty conference +%% style file. The constants in it are somewhat magical, and appear +%% to work well with the two-column format on US letter paper that +%% ICML uses, but will break if you change that layout, or if you use +%% a longer block of text for the copyright notice string. Fiddle with +%% them if necessary to get the block to fit/look right. +%% +%% -- Terran Lane, 2003 +%% +%% The following comments are included verbatim from acmconf.sty: +%% +%%% This section (written by KBT) handles the 1" box in the lower left +%%% corner of the left column of the first page by creating a picture, +%%% and inserting the predefined string at the bottom (with a negative +%%% displacement to offset the space allocated for a non-existent +%%% caption). +%%% +\def\ftype@copyrightbox{8} +\def\@copyrightspace{ +% Create a float object positioned at the bottom of the column. Note +% that because of the mystical nature of floats, this has to be called +% before the first column is populated with text (e.g., from the title +% or abstract blocks). Otherwise, the text will force the float to +% the next column. -- TDRL. +\@float{copyrightbox}[b] +\begin{center} +\setlength{\unitlength}{1pc} +\begin{picture}(20,1.5) +% Create a line separating the main text from the note block. +% 4.818pc==0.8in. +\put(0,2.5){\line(1,0){4.818}} +% Insert the text string itself. Note that the string has to be +% enclosed in a parbox -- the \put call needs a box object to +% position. Without the parbox, the text gets splattered across the +% bottom of the page semi-randomly. The 19.75pc distance seems to be +% the width of the column, though I can't find an appropriate distance +% variable to substitute here. -- TDRL. +\put(0,0){\parbox[b]{19.75pc}{\small \Notice@String}} +\end{picture} +\end{center} +\end@float} + +% Note: A few Latex versions need the next line instead of the former. +% \addtolength{\topmargin}{0.3in} +% \setlength\footheight{0pt} +\setlength\footskip{25.0pt} +%\pagestyle{empty} +\flushbottom \twocolumn +\sloppy + +% Clear out the addcontentsline command +\def\addcontentsline#1#2#3{} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% commands for formatting paper title, author names, and addresses. + +%%start%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%% title as running head -- Kristian Kersting 2005 %%%%%%%%%%%%% + + +%\makeatletter +%\newtoks\mytoksa +%\newtoks\mytoksb +%\newcommand\addtomylist[2]{% +% \mytoksa\expandafter{#1}% +% \mytoksb{#2}% +% \edef#1{\the\mytoksa\the\mytoksb}% +%} +%\makeatother + +% box to check the size of the running head +\newbox\titrun + +% general page style +\pagestyle{fancy} +\fancyhf{} +\fancyhead{} +\fancyfoot{} +\cfoot{\thepage} +% set the width of the head rule to 1 point +\renewcommand{\headrulewidth}{1pt} + +% definition to set the head as running head in the preamble +\def\icmltitlerunning#1{\gdef\@icmltitlerunning{#1}} + +% main definition adapting \icmltitle from 2004 +\long\def\icmltitle#1{% + + %check whether @icmltitlerunning exists + % if not \icmltitle is used as running head + \ifx\undefined\@icmltitlerunning% + \gdef\@icmltitlerunning{#1} + \fi + + %add it to pdf information + \ifdefined\nohyperref\else\ifdefined\hypersetup + \hypersetup{pdftitle={#1}} + \fi\fi + + %get the dimension of the running title + \global\setbox\titrun=\vbox{\small\bf\@icmltitlerunning} + + % error flag + \gdef\@runningtitleerror{0} + + % running title too long + \ifdim\wd\titrun>\textwidth% + {\gdef\@runningtitleerror{1}}% + % running title breaks a line + \else\ifdim\ht\titrun>6.25pt + {\gdef\@runningtitleerror{2}}% + \fi + \fi + + % if there is somthing wrong with the running title + \ifnum\@runningtitleerror>0 + \typeout{}% + \typeout{}% + \typeout{*******************************************************}% + \typeout{Title exceeds size limitations for running head.}% + \typeout{Please supply a shorter form for the running head} + \typeout{with \string\icmltitlerunning{...}\space prior to \string\begin{document}}% + \typeout{*******************************************************}% + \typeout{}% + \typeout{}% + % set default running title + \chead{\small\bf Title Suppressed Due to Excessive Size}% + \else + % 'everything' fine, set provided running title + \chead{\small\bf\@icmltitlerunning}% + \fi + + % no running title on the first page of the paper + \thispagestyle{plain} + +%%%%%%%%%%%%%%%%%%%% Kristian Kersting %%%%%%%%%%%%%%%%%%%%%%%%% +%end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + {\center\baselineskip 18pt + \toptitlebar{\Large\bf #1}\bottomtitlebar} +} + + +\gdef\icmlfullauthorlist{} +\newcommand\addstringtofullauthorlist{\g@addto@macro\icmlfullauthorlist} +\newcommand\addtofullauthorlist[1]{% + \ifdefined\icmlanyauthors% + \addstringtofullauthorlist{, #1}% + \else% + \addstringtofullauthorlist{#1}% + \gdef\icmlanyauthors{1}% + \fi% +% \ifdefined\nohyperref\else + \ifdefined\hypersetup% + \hypersetup{pdfauthor=\icmlfullauthorlist}% + \fi%\fi + } + + +\def\toptitlebar{\hrule height1pt \vskip .25in} +\def\bottomtitlebar{\vskip .22in \hrule height1pt \vskip .3in} + +\newenvironment{icmlauthorlist}{% + \setlength\topsep{0pt} + \setlength\parskip{0pt} + \begin{center} +}{% + \end{center} +} + +\newcounter{@affiliationcounter} +\newcommand{\@pa}[1]{% +% ``#1'' +\ifcsname the@affil#1\endcsname + % do nothing +\else + \ifcsname @icmlsymbol#1\endcsname + % nothing + \else + \stepcounter{@affiliationcounter}% + \newcounter{@affil#1}% + \setcounter{@affil#1}{\value{@affiliationcounter}}% + \fi +\fi% +\ifcsname @icmlsymbol#1\endcsname + \textsuperscript{\csname @icmlsymbol#1\endcsname\,}% +\else + %\expandafter\footnotemark[\arabic{@affil#1}\,]% + \textsuperscript{\arabic{@affil#1}\,}% +\fi +} + +%\newcommand{\icmlauthor}[2]{% +%\addtofullauthorlist{#1}% +%#1\@for\theaffil:=#2\do{\pa{\theaffil}}% +%} +\newcommand{\icmlauthor}[2]{% + \ifdefined\isaccepted + \mbox{\bf #1}\,\@for\theaffil:=#2\do{\@pa{\theaffil}} \addtofullauthorlist{#1}% + \else + \ifdefined\@icmlfirsttime + \else + \gdef\@icmlfirsttime{1} + \mbox{\bf Anonymous Authors}\@pa{@anon} \addtofullauthorlist{Anonymous Authors} + \fi + \fi +} + + + + +\newcommand{\icmlsetsymbol}[2]{% + \expandafter\gdef\csname @icmlsymbol#1\endcsname{#2} + } + + +\newcommand{\icmlaffiliation}[2]{% +\ifdefined\isaccepted +\ifcsname the@affil#1\endcsname + \expandafter\gdef\csname @affilname\csname the@affil#1\endcsname\endcsname{#2}% +\else + {\bf AUTHORERR: Error in use of \textbackslash{}icmlaffiliation command. Label ``#1'' not mentioned in some \textbackslash{}icmlauthor\{author name\}\{labels here\} command beforehand. } + \typeout{}% + \typeout{}% + \typeout{*******************************************************}% + \typeout{Affiliation label undefined. }% + \typeout{Make sure \string\icmlaffiliation\space follows } + \typeout{all of \string\icmlauthor\space commands}% + \typeout{*******************************************************}% + \typeout{}% + \typeout{}% +\fi +\else % \isaccepted + % can be called multiple times... it's idempotent + \expandafter\gdef\csname @affilname1\endcsname{Anonymous Institution, Anonymous City, Anonymous Region, Anonymous Country} +\fi +} + +\newcommand{\icmlcorrespondingauthor}[2]{ +\ifdefined\isaccepted + \ifdefined\icmlcorrespondingauthor@text + \g@addto@macro\icmlcorrespondingauthor@text{, #1 \textless{}#2\textgreater{}} + \else + \gdef\icmlcorrespondingauthor@text{#1 \textless{}#2\textgreater{}} + \fi +\else +\gdef\icmlcorrespondingauthor@text{Anonymous Author \textless{}anon.email@domain.com\textgreater{}} +\fi +} + +\newcommand{\icmlEqualContribution}{\textsuperscript{*}Equal contribution } + +\newcounter{@affilnum} +\newcommand{\printAffiliationsAndNotice}[1]{% +\stepcounter{@affiliationcounter}% +{\let\thefootnote\relax\footnotetext{\hspace*{-\footnotesep}\ifdefined\isaccepted #1\fi% +\forloop{@affilnum}{1}{\value{@affilnum} < \value{@affiliationcounter}}{ +\textsuperscript{\arabic{@affilnum}}\ifcsname @affilname\the@affilnum\endcsname% +\csname @affilname\the@affilnum\endcsname% +\else +{\bf AUTHORERR: Missing \textbackslash{}icmlaffiliation.} +\fi +}. +\ifdefined\icmlcorrespondingauthor@text +Correspondence to: \icmlcorrespondingauthor@text. +\else +{\bf AUTHORERR: Missing \textbackslash{}icmlcorrespondingauthor.} +\fi + +\ \\ +\Notice@String +} +} +} + +%\makeatother + +\long\def\icmladdress#1{% + {\bf The \textbackslash{}icmladdress command is no longer used. See the example\_paper PDF .tex for usage of \textbackslash{}icmlauther and \textbackslash{}icmlaffiliation.} +} + +%% keywords as first class citizens +\def\icmlkeywords#1{% +% \ifdefined\isaccepted \else +% \par {\bf Keywords:} #1% +% \fi +% \ifdefined\nohyperref\else\ifdefined\hypersetup +% \hypersetup{pdfkeywords={#1}} +% \fi\fi +% \ifdefined\isaccepted \else +% \par {\bf Keywords:} #1% +% \fi + \ifdefined\nohyperref\else\ifdefined\hypersetup + \hypersetup{pdfkeywords={#1}} + \fi\fi +} + +% modification to natbib citations +\setcitestyle{authoryear,round,citesep={;},aysep={,},yysep={;}} + +% Redefinition of the abstract environment. +\renewenvironment{abstract} + {% +% Insert the ``appearing in'' copyright notice. +%\@copyrightspace +\centerline{\large\bf Abstract} + \vspace{-0.12in}\begin{quote}} + {\par\end{quote}\vskip 0.12in} + +% numbered section headings with different treatment of numbers + +\def\@startsection#1#2#3#4#5#6{\if@noskipsec \leavevmode \fi + \par \@tempskipa #4\relax + \@afterindenttrue +% Altered the following line to indent a section's first paragraph. +% \ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \@afterindentfalse\fi + \ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \fi + \if@nobreak \everypar{}\else + \addpenalty{\@secpenalty}\addvspace{\@tempskipa}\fi \@ifstar + {\@ssect{#3}{#4}{#5}{#6}}{\@dblarg{\@sict{#1}{#2}{#3}{#4}{#5}{#6}}}} + +\def\@sict#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth + \def\@svsec{}\else + \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname}\fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup #6\relax + \@hangfrom{\hskip #3\relax\@svsec.~}{\interlinepenalty \@M #8\par} + \endgroup + \csname #1mark\endcsname{#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}\else + \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname + {#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}}\fi + \@xsect{#5}} + +\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth + \def\@svsec{}\else + \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname\hskip 0.4em }\fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup #6\relax + \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par} + \endgroup + \csname #1mark\endcsname{#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}\else + \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname + {#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}}\fi + \@xsect{#5}} + +% section headings with less space above and below them +\def\thesection {\arabic{section}} +\def\thesubsection {\thesection.\arabic{subsection}} +\def\section{\@startsection{section}{1}{\z@}{-0.12in}{0.02in} + {\large\bf\raggedright}} +\def\subsection{\@startsection{subsection}{2}{\z@}{-0.10in}{0.01in} + {\normalsize\bf\raggedright}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-0.08in}{0.01in} + {\normalsize\sc\raggedright}} +\def\paragraph{\@startsection{paragraph}{4}{\z@}{1.5ex plus + 0.5ex minus .2ex}{-1em}{\normalsize\bf}} +\def\subparagraph{\@startsection{subparagraph}{5}{\z@}{1.5ex plus + 0.5ex minus .2ex}{-1em}{\normalsize\bf}} + +% Footnotes +\footnotesep 6.65pt % +\skip\footins 9pt +\def\footnoterule{\kern-3pt \hrule width 0.8in \kern 2.6pt } +\setcounter{footnote}{0} + +% Lists and paragraphs +\parindent 0pt +\topsep 4pt plus 1pt minus 2pt +\partopsep 1pt plus 0.5pt minus 0.5pt +\itemsep 2pt plus 1pt minus 0.5pt +\parsep 2pt plus 1pt minus 0.5pt +\parskip 6pt + +\leftmargin 2em \leftmargini\leftmargin \leftmarginii 2em +\leftmarginiii 1.5em \leftmarginiv 1.0em \leftmarginv .5em +\leftmarginvi .5em +\labelwidth\leftmargini\advance\labelwidth-\labelsep \labelsep 5pt + +\def\@listi{\leftmargin\leftmargini} +\def\@listii{\leftmargin\leftmarginii + \labelwidth\leftmarginii\advance\labelwidth-\labelsep + \topsep 2pt plus 1pt minus 0.5pt + \parsep 1pt plus 0.5pt minus 0.5pt + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii\advance\labelwidth-\labelsep + \topsep 1pt plus 0.5pt minus 0.5pt + \parsep \z@ \partopsep 0.5pt plus 0pt minus 0.5pt + \itemsep \topsep} +\def\@listiv{\leftmargin\leftmarginiv + \labelwidth\leftmarginiv\advance\labelwidth-\labelsep} +\def\@listv{\leftmargin\leftmarginv + \labelwidth\leftmarginv\advance\labelwidth-\labelsep} +\def\@listvi{\leftmargin\leftmarginvi + \labelwidth\leftmarginvi\advance\labelwidth-\labelsep} + +\abovedisplayskip 7pt plus2pt minus5pt% +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip 0pt plus3pt% +\belowdisplayshortskip 4pt plus3pt minus3pt% + +% Less leading in most fonts (due to the narrow columns) +% The choices were between 1-pt and 1.5-pt leading +\def\@normalsize{\@setsize\normalsize{11pt}\xpt\@xpt} +\def\small{\@setsize\small{10pt}\ixpt\@ixpt} +\def\footnotesize{\@setsize\footnotesize{10pt}\ixpt\@ixpt} +\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt} +\def\tiny{\@setsize\tiny{7pt}\vipt\@vipt} +\def\large{\@setsize\large{14pt}\xiipt\@xiipt} +\def\Large{\@setsize\Large{16pt}\xivpt\@xivpt} +\def\LARGE{\@setsize\LARGE{20pt}\xviipt\@xviipt} +\def\huge{\@setsize\huge{23pt}\xxpt\@xxpt} +\def\Huge{\@setsize\Huge{28pt}\xxvpt\@xxvpt} + +% Revised formatting for figure captions and table titles. +\newsavebox\newcaptionbox\newdimen\newcaptionboxwid + +\long\def\@makecaption#1#2{ + \vskip 10pt + \baselineskip 11pt + \setbox\@tempboxa\hbox{#1. #2} + \ifdim \wd\@tempboxa >\hsize + \sbox{\newcaptionbox}{\small\sl #1.~} + \newcaptionboxwid=\wd\newcaptionbox + \usebox\newcaptionbox {\footnotesize #2} +% \usebox\newcaptionbox {\small #2} + \else + \centerline{{\small\sl #1.} {\small #2}} + \fi} + +\def\fnum@figure{Figure \thefigure} +\def\fnum@table{Table \thetable} + +% Strut macros for skipping spaces above and below text in tables. +\def\abovestrut#1{\rule[0in]{0in}{#1}\ignorespaces} +\def\belowstrut#1{\rule[-#1]{0in}{#1}\ignorespaces} + +\def\abovespace{\abovestrut{0.20in}} +\def\aroundspace{\abovestrut{0.20in}\belowstrut{0.10in}} +\def\belowspace{\belowstrut{0.10in}} + +% Various personal itemization commands. +\def\texitem#1{\par\noindent\hangindent 12pt + \hbox to 12pt {\hss #1 ~}\ignorespaces} +\def\icmlitem{\texitem{$\bullet$}} + +% To comment out multiple lines of text. +\long\def\comment#1{} + + + + +%% Line counter (not in final version). Adapted from NIPS style file by Christoph Sawade + +% Vertical Ruler +% This code is, largely, from the CVPR 2010 conference style file +% ----- define vruler +\makeatletter +\newbox\icmlrulerbox +\newcount\icmlrulercount +\newdimen\icmlruleroffset +\newdimen\cv@lineheight +\newdimen\cv@boxheight +\newbox\cv@tmpbox +\newcount\cv@refno +\newcount\cv@tot +% NUMBER with left flushed zeros \fillzeros[] +\newcount\cv@tmpc@ \newcount\cv@tmpc +\def\fillzeros[#1]#2{\cv@tmpc@=#2\relax\ifnum\cv@tmpc@<0\cv@tmpc@=-\cv@tmpc@\fi +\cv@tmpc=1 % +\loop\ifnum\cv@tmpc@<10 \else \divide\cv@tmpc@ by 10 \advance\cv@tmpc by 1 \fi + \ifnum\cv@tmpc@=10\relax\cv@tmpc@=11\relax\fi \ifnum\cv@tmpc@>10 \repeat +\ifnum#2<0\advance\cv@tmpc1\relax-\fi +\loop\ifnum\cv@tmpc<#1\relax0\advance\cv@tmpc1\relax\fi \ifnum\cv@tmpc<#1 \repeat +\cv@tmpc@=#2\relax\ifnum\cv@tmpc@<0\cv@tmpc@=-\cv@tmpc@\fi \relax\the\cv@tmpc@}% +% \makevruler[][][][][] +\def\makevruler[#1][#2][#3][#4][#5]{ + \begingroup\offinterlineskip + \textheight=#5\vbadness=10000\vfuzz=120ex\overfullrule=0pt% + \global\setbox\icmlrulerbox=\vbox to \textheight{% + { + \parskip=0pt\hfuzz=150em\cv@boxheight=\textheight + \cv@lineheight=#1\global\icmlrulercount=#2% + \cv@tot\cv@boxheight\divide\cv@tot\cv@lineheight\advance\cv@tot2% + \cv@refno1\vskip-\cv@lineheight\vskip1ex% + \loop\setbox\cv@tmpbox=\hbox to0cm{ % side margin + \hfil {\hfil\fillzeros[#4]\icmlrulercount} + }% + \ht\cv@tmpbox\cv@lineheight\dp\cv@tmpbox0pt\box\cv@tmpbox\break + \advance\cv@refno1\global\advance\icmlrulercount#3\relax + \ifnum\cv@refno<\cv@tot\repeat + } + } + \endgroup +}% +\makeatother +% ----- end of vruler + + +% \makevruler[][][][][] +\def\icmlruler#1{\makevruler[12pt][#1][1][3][\textheight]\usebox{\icmlrulerbox}} +\AddToShipoutPicture{% +\icmlruleroffset=\textheight +\advance\icmlruleroffset by 5.2pt % top margin + \color[rgb]{.7,.7,.7} + \ifdefined\isaccepted \else + \AtTextUpperLeft{% + \put(\LenToUnit{-35pt},\LenToUnit{-\icmlruleroffset}){%left ruler + \icmlruler{\icmlrulercount}} +% \put(\LenToUnit{1.04\textwidth},\LenToUnit{-\icmlruleroffset}){%right ruler +% \icmlruler{\icmlrulercount}} + } + \fi +} +\endinput diff --git a/docs/ICML_workshop/icml2023-diffxyz/icml2023.bst b/docs/ICML_workshop/icml2023-diffxyz/icml2023.bst new file mode 100644 index 0000000..070cf4a --- /dev/null +++ b/docs/ICML_workshop/icml2023-diffxyz/icml2023.bst @@ -0,0 +1,1443 @@ +%% File: `icml2023.bst' +%% A modification of `plainnl.bst' for use with natbib package +%% +%% Copyright 2010 Hal Daum\'e III +%% Modified by J. Fürnkranz +%% - Changed labels from (X and Y, 2000) to (X & Y, 2000) +%% - Changed References to last name first and abbreviated first names. +%% Modified by Iain Murray 2018 (who suggests adopting a standard .bst in future...) +%% - Made it actually use abbreviated first names +%% +%% Copyright 1993-2007 Patrick W Daly +%% Max-Planck-Institut f\"ur Sonnensystemforschung +%% Max-Planck-Str. 2 +%% D-37191 Katlenburg-Lindau +%% Germany +%% E-mail: daly@mps.mpg.de +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN +%% archives in directory macros/latex/base/lppl.txt; either +%% version 1 of the License, or any later version. +%% + % Version and source file information: + % \ProvidesFile{icml2010.mbs}[2007/11/26 1.93 (PWD)] + % + % BibTeX `plainnat' family + % version 0.99b for BibTeX versions 0.99a or later, + % for LaTeX versions 2.09 and 2e. + % + % For use with the `natbib.sty' package; emulates the corresponding + % member of the `plain' family, but with author-year citations. + % + % With version 6.0 of `natbib.sty', it may also be used for numerical + % citations, while retaining the commands \citeauthor, \citefullauthor, + % and \citeyear to print the corresponding information. + % + % For version 7.0 of `natbib.sty', the KEY field replaces missing + % authors/editors, and the date is left blank in \bibitem. + % + % Includes field EID for the sequence/citation number of electronic journals + % which is used instead of page numbers. + % + % Includes fields ISBN and ISSN. + % + % Includes field URL for Internet addresses. + % + % Includes field DOI for Digital Object Idenfifiers. + % + % Works best with the url.sty package of Donald Arseneau. + % + % Works with identical authors and year are further sorted by + % citation key, to preserve any natural sequence. + % +ENTRY + { address + author + booktitle + chapter + doi + eid + edition + editor + howpublished + institution + isbn + issn + journal + key + month + note + number + organization + pages + publisher + school + series + title + type + url + volume + year + } + {} + { label extra.label sort.label short.list } + +INTEGERS { output.state before.all mid.sentence after.sentence after.block } + +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} + +STRINGS { s t } + +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} + +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} + +FUNCTION {new.block.checka} +{ empty$ + 'skip$ + 'new.block + if$ +} + +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} + +FUNCTION {new.sentence.checka} +{ empty$ + 'skip$ + 'new.sentence + if$ +} + +FUNCTION {new.sentence.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.sentence + if$ +} + +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} + +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "\emph{" swap$ * "}" * } + if$ +} + +INTEGERS { nameptr namesleft numnames } + +FUNCTION {format.names} +{ 's := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr "{vv~}{ll}{, jj}{, f.}" format.name$ 't := + nameptr #1 > + { namesleft #1 > + { ", " * t * } + { numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {format.key} +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.authors} +{ author empty$ + { "" } + { author format.names } + if$ +} + +FUNCTION {format.editors} +{ editor empty$ + { "" } + { editor format.names + editor num.names$ #1 > + { " (eds.)" * } + { " (ed.)" * } + if$ + } + if$ +} + +FUNCTION {format.isbn} +{ isbn empty$ + { "" } + { new.block "ISBN " isbn * } + if$ +} + +FUNCTION {format.issn} +{ issn empty$ + { "" } + { new.block "ISSN " issn * } + if$ +} + +FUNCTION {format.url} +{ url empty$ + { "" } + { new.block "URL \url{" url * "}" * } + if$ +} + +FUNCTION {format.doi} +{ doi empty$ + { "" } + { new.block "\doi{" doi * "}" * } + if$ +} + +FUNCTION {format.title} +{ title empty$ + { "" } + { title "t" change.case$ } + if$ +} + +FUNCTION {format.full.names} +{'s := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}" format.name$ 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {author.editor.full} +{ author empty$ + { editor empty$ + { "" } + { editor format.full.names } + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {author.full} +{ author empty$ + { "" } + { author format.full.names } + if$ +} + +FUNCTION {editor.full} +{ editor empty$ + { "" } + { editor format.full.names } + if$ +} + +FUNCTION {make.full.names} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.full + { type$ "proceedings" = + 'editor.full + 'author.full + if$ + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[" write$ + label write$ + ")" make.full.names duplicate$ short.list = + { pop$ } + { * } + if$ + "]{" * write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {n.dashify} +{ 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {format.date} +{ year duplicate$ empty$ + { "empty year in " cite$ * warning$ + pop$ "" } + 'skip$ + if$ + month empty$ + 'skip$ + { month + " " * swap$ * + } + if$ + extra.label * +} + +FUNCTION {format.btitle} +{ title emphasize +} + +FUNCTION {tie.or.space.connect} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ * * +} + +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { "volume" volume tie.or.space.connect + series empty$ + 'skip$ + { " of " * series emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} + +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { output.state mid.sentence = + { "number" } + { "Number" } + if$ + number tie.or.space.connect + series empty$ + { "there's a number but no series in " cite$ * warning$ } + { " in " * series * } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {format.edition} +{ edition empty$ + { "" } + { output.state mid.sentence = + { edition "l" change.case$ " edition" * } + { edition "t" change.case$ " edition" * } + if$ + } + if$ +} + +INTEGERS { multiresult } + +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {format.pages} +{ pages empty$ + { "" } + { pages multi.page.check + { "pp.\ " pages n.dashify tie.or.space.connect } + { "pp.\ " pages tie.or.space.connect } + if$ + } + if$ +} + +FUNCTION {format.eid} +{ eid empty$ + { "" } + { "art." eid tie.or.space.connect } + if$ +} + +FUNCTION {format.vol.num.pages} +{ volume field.or.null + number empty$ + 'skip$ + { "\penalty0 (" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + pages empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.pages } + { ":\penalty0 " * pages n.dashify * } + if$ + } + if$ +} + +FUNCTION {format.vol.num.eid} +{ volume field.or.null + number empty$ + 'skip$ + { "\penalty0 (" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + eid empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.eid } + { ":\penalty0 " * eid * } + if$ + } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + 'format.pages + { type empty$ + { "chapter" } + { type "l" change.case$ } + if$ + chapter tie.or.space.connect + pages empty$ + 'skip$ + { ", " * format.pages * } + if$ + } + if$ +} + +FUNCTION {format.in.ed.booktitle} +{ booktitle empty$ + { "" } + { editor empty$ + { "In " booktitle emphasize * } + { "In " format.editors * ", " * booktitle emphasize * } + if$ + } + if$ +} + +FUNCTION {empty.misc.check} +{ author empty$ title empty$ howpublished empty$ + month empty$ year empty$ note empty$ + and and and and and + key empty$ not and + { "all relevant fields are empty in " cite$ * warning$ } + 'skip$ + if$ +} + +FUNCTION {format.thesis.type} +{ type empty$ + 'skip$ + { pop$ + type "t" change.case$ + } + if$ +} + +FUNCTION {format.tr.number} +{ type empty$ + { "Technical Report" } + 'type + if$ + number empty$ + { "t" change.case$ } + { number tie.or.space.connect } + if$ +} + +FUNCTION {format.article.crossref} +{ key empty$ + { journal empty$ + { "need key or journal for " cite$ * " to crossref " * crossref * + warning$ + "" + } + { "In \emph{" journal * "}" * } + if$ + } + { "In " } + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {format.book.crossref} +{ volume empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + "In " + } + { "Volume" volume tie.or.space.connect + " of " * + } + if$ + editor empty$ + editor field.or.null author field.or.null = + or + { key empty$ + { series empty$ + { "need editor, key, or series for " cite$ * " to crossref " * + crossref * warning$ + "" * + } + { "\emph{" * series * "}" * } + if$ + } + 'skip$ + if$ + } + 'skip$ + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {format.incoll.inproc.crossref} +{ editor empty$ + editor field.or.null author field.or.null = + or + { key empty$ + { booktitle empty$ + { "need editor, key, or booktitle for " cite$ * " to crossref " * + crossref * warning$ + "" + } + { "In \emph{" booktitle * "}" * } + if$ + } + { "In " } + if$ + } + { "In " } + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {article} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { journal emphasize "journal" output.check + eid empty$ + { format.vol.num.pages output } + { format.vol.num.eid output } + if$ + format.date "year" output.check + } + { format.article.crossref output.nonnull + eid empty$ + { format.pages output } + { format.eid output } + if$ + } + if$ + format.issn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {book} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.date "year" output.check + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {booklet} +{ output.bibitem + format.authors output + author format.key output + new.block + format.title "title" output.check + howpublished address new.block.checkb + howpublished output + address output + format.date output + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {inbook} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + format.chapter.pages "chapter and pages" output.check + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { format.chapter.pages "chapter and pages" output.check + new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.date "year" output.check + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {incollection} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.chapter.pages output + new.sentence + publisher "publisher" output.check + address output + format.edition output + format.date "year" output.check + } + { format.incoll.inproc.crossref output.nonnull + format.chapter.pages output + } + if$ + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {inproceedings} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.pages output + address empty$ + { organization publisher new.sentence.checkb + organization output + publisher output + format.date "year" output.check + } + { address output.nonnull + format.date "year" output.check + new.sentence + organization output + publisher output + } + if$ + } + { format.incoll.inproc.crossref output.nonnull + format.pages output + } + if$ + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {conference} { inproceedings } + +FUNCTION {manual} +{ output.bibitem + format.authors output + author format.key output + new.block + format.btitle "title" output.check + organization address new.block.checkb + organization output + address output + format.edition output + format.date output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {mastersthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + "Master's thesis" format.thesis.type output.nonnull + school "school" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {misc} +{ output.bibitem + format.authors output + author format.key output + title howpublished new.block.checkb + format.title output + howpublished new.block.checka + howpublished output + format.date output + format.issn output + format.url output + new.block + note output + fin.entry + empty.misc.check +} + +FUNCTION {phdthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.btitle "title" output.check + new.block + "PhD thesis" format.thesis.type output.nonnull + school "school" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {proceedings} +{ output.bibitem + format.editors output + editor format.key output + new.block + format.btitle "title" output.check + format.bvolume output + format.number.series output + address output + format.date "year" output.check + new.sentence + organization output + publisher output + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {techreport} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + format.tr.number output.nonnull + institution "institution" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {unpublished} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + note "note" output.check + format.date output + format.url output + fin.entry +} + +FUNCTION {default.type} { misc } + + +MACRO {jan} {"January"} + +MACRO {feb} {"February"} + +MACRO {mar} {"March"} + +MACRO {apr} {"April"} + +MACRO {may} {"May"} + +MACRO {jun} {"June"} + +MACRO {jul} {"July"} + +MACRO {aug} {"August"} + +MACRO {sep} {"September"} + +MACRO {oct} {"October"} + +MACRO {nov} {"November"} + +MACRO {dec} {"December"} + + + +MACRO {acmcs} {"ACM Computing Surveys"} + +MACRO {acta} {"Acta Informatica"} + +MACRO {cacm} {"Communications of the ACM"} + +MACRO {ibmjrd} {"IBM Journal of Research and Development"} + +MACRO {ibmsj} {"IBM Systems Journal"} + +MACRO {ieeese} {"IEEE Transactions on Software Engineering"} + +MACRO {ieeetc} {"IEEE Transactions on Computers"} + +MACRO {ieeetcad} + {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"} + +MACRO {ipl} {"Information Processing Letters"} + +MACRO {jacm} {"Journal of the ACM"} + +MACRO {jcss} {"Journal of Computer and System Sciences"} + +MACRO {scp} {"Science of Computer Programming"} + +MACRO {sicomp} {"SIAM Journal on Computing"} + +MACRO {tocs} {"ACM Transactions on Computer Systems"} + +MACRO {tods} {"ACM Transactions on Database Systems"} + +MACRO {tog} {"ACM Transactions on Graphics"} + +MACRO {toms} {"ACM Transactions on Mathematical Software"} + +MACRO {toois} {"ACM Transactions on Office Information Systems"} + +MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"} + +MACRO {tcs} {"Theoretical Computer Science"} + + +READ + +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} + +INTEGERS { len } + +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} + +FUNCTION {format.lab.names} +{ 's := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ " et~al." * } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { " et~al." * } + { " \& " * s #2 "{vv~}{ll}" format.name$ * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.key.organization.label} +{ author empty$ + { key empty$ + { organization empty$ + { cite$ #1 #3 substring$ } + { "The " #4 organization chop.word #3 text.prefix$ } + if$ + } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.organization.label} +{ editor empty$ + { key empty$ + { organization empty$ + { cite$ #1 #3 substring$ } + { "The " #4 organization chop.word #3 text.prefix$ } + if$ + } + 'key + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.short.authors} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.organization.label + { type$ "manual" = + 'author.key.organization.label + 'author.key.label + if$ + } + if$ + } + if$ + 'short.list := +} + +FUNCTION {calc.label} +{ calc.short.authors + short.list + "(" + * + year duplicate$ empty$ + short.list key field.or.null = or + { pop$ "" } + 'skip$ + if$ + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { + s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't := + nameptr #1 > + { + " " * + namesleft #1 = t "others" = and + { "zzzzz" * } + { numnames #2 > nameptr #2 = and + { "zz" * year field.or.null * " " * } + 'skip$ + if$ + t sortify * + } + if$ + } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} + +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.organization.sort} +{ author empty$ + { organization empty$ + { key empty$ + { "to sort, need author, organization, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { "The " #4 organization chop.word sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {editor.organization.sort} +{ editor empty$ + { organization empty$ + { key empty$ + { "to sort, need editor, organization, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { "The " #4 organization chop.word sortify } + if$ + } + { editor sort.format.names } + if$ +} + + +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.organization.sort + { type$ "manual" = + 'author.organization.sort + 'author.sort + if$ + } + if$ + } + if$ + " " + * + year field.or.null sortify + * + " " + * + cite$ + * + #1 entry.max$ substring$ + 'sort.label := + sort.label * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} + +SORT + +STRINGS { longest.label last.label next.extra } + +INTEGERS { longest.label.width last.extra.num number.label } + +FUNCTION {initialize.longest.label} +{ "" 'longest.label := + #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'longest.label.width := + #0 'last.extra.num := + #0 'number.label := +} + +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ + number.label #1 + 'number.label := +} + +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + extra.label 'next.extra := + extra.label + duplicate$ empty$ + 'skip$ + { "{\natexlab{" swap$ * "}}" * } + if$ + 'extra.label := + label extra.label * 'label := +} + +EXECUTE {initialize.longest.label} + +ITERATE {forward.pass} + +REVERSE {reverse.pass} + +FUNCTION {bib.sort.order} +{ sort.label 'sort.key$ := +} + +ITERATE {bib.sort.order} + +SORT + +FUNCTION {begin.bib} +{ preamble$ empty$ + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" number.label int.to.str$ * "}" * + write$ newline$ + "\providecommand{\natexlab}[1]{#1}" + write$ newline$ + "\providecommand{\url}[1]{\texttt{#1}}" + write$ newline$ + "\expandafter\ifx\csname urlstyle\endcsname\relax" + write$ newline$ + " \providecommand{\doi}[1]{doi: #1}\else" + write$ newline$ + " \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi" + write$ newline$ +} + +EXECUTE {begin.bib} + +EXECUTE {init.state.consts} + +ITERATE {call.type$} + +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} + +EXECUTE {end.bib} diff --git a/docs/ICML_workshop/icml2023/algorithm.sty b/docs/ICML_workshop/icml2023/algorithm.sty new file mode 100644 index 0000000..a723c1c --- /dev/null +++ b/docs/ICML_workshop/icml2023/algorithm.sty @@ -0,0 +1,79 @@ +% ALGORITHM STYLE -- Released 8 April 1996 +% for LaTeX-2e +% Copyright -- 1994 Peter Williams +% E-mail Peter.Williams@dsto.defence.gov.au +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithm} +\typeout{Document Style `algorithm' - floating environment} + +\RequirePackage{float} +\RequirePackage{ifthen} +\newcommand{\ALG@within}{nothing} +\newboolean{ALG@within} +\setboolean{ALG@within}{false} +\newcommand{\ALG@floatstyle}{ruled} +\newcommand{\ALG@name}{Algorithm} +\newcommand{\listalgorithmname}{List of \ALG@name s} + +% Declare Options +% first appearance +\DeclareOption{plain}{ + \renewcommand{\ALG@floatstyle}{plain} +} +\DeclareOption{ruled}{ + \renewcommand{\ALG@floatstyle}{ruled} +} +\DeclareOption{boxed}{ + \renewcommand{\ALG@floatstyle}{boxed} +} +% then numbering convention +\DeclareOption{part}{ + \renewcommand{\ALG@within}{part} + \setboolean{ALG@within}{true} +} +\DeclareOption{chapter}{ + \renewcommand{\ALG@within}{chapter} + \setboolean{ALG@within}{true} +} +\DeclareOption{section}{ + \renewcommand{\ALG@within}{section} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsection}{ + \renewcommand{\ALG@within}{subsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsubsection}{ + \renewcommand{\ALG@within}{subsubsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{nothing}{ + \renewcommand{\ALG@within}{nothing} + \setboolean{ALG@within}{true} +} +\DeclareOption*{\edef\ALG@name{\CurrentOption}} + +% ALGORITHM +% +\ProcessOptions +\floatstyle{\ALG@floatstyle} +\ifthenelse{\boolean{ALG@within}}{ + \ifthenelse{\equal{\ALG@within}{part}} + {\newfloat{algorithm}{htbp}{loa}[part]}{} + \ifthenelse{\equal{\ALG@within}{chapter}} + {\newfloat{algorithm}{htbp}{loa}[chapter]}{} + \ifthenelse{\equal{\ALG@within}{section}} + {\newfloat{algorithm}{htbp}{loa}[section]}{} + \ifthenelse{\equal{\ALG@within}{subsection}} + {\newfloat{algorithm}{htbp}{loa}[subsection]}{} + \ifthenelse{\equal{\ALG@within}{subsubsection}} + {\newfloat{algorithm}{htbp}{loa}[subsubsection]}{} + \ifthenelse{\equal{\ALG@within}{nothing}} + {\newfloat{algorithm}{htbp}{loa}}{} +}{ + \newfloat{algorithm}{htbp}{loa} +} +\floatname{algorithm}{\ALG@name} + +\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}} + diff --git a/docs/ICML_workshop/icml2023/algorithmic.sty b/docs/ICML_workshop/icml2023/algorithmic.sty new file mode 100644 index 0000000..e2502a6 --- /dev/null +++ b/docs/ICML_workshop/icml2023/algorithmic.sty @@ -0,0 +1,201 @@ +% ALGORITHMIC STYLE -- Released 8 APRIL 1996 +% for LaTeX version 2e +% Copyright -- 1994 Peter Williams +% E-mail PeterWilliams@dsto.defence.gov.au +% +% Modified by Alex Smola (08/2000) +% E-mail Alex.Smola@anu.edu.au +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithmic} +\typeout{Document Style `algorithmic' - environment} +% +\RequirePackage{ifthen} +\RequirePackage{calc} +\newboolean{ALC@noend} +\setboolean{ALC@noend}{false} +\newcounter{ALC@line} +\newcounter{ALC@rem} +\newlength{\ALC@tlm} +% +\DeclareOption{noend}{\setboolean{ALC@noend}{true}} +% +\ProcessOptions +% +% ALGORITHMIC +\newcommand{\algorithmicrequire}{\textbf{Require:}} +\newcommand{\algorithmicensure}{\textbf{Ensure:}} +\newcommand{\algorithmiccomment}[1]{\{#1\}} +\newcommand{\algorithmicend}{\textbf{end}} +\newcommand{\algorithmicif}{\textbf{if}} +\newcommand{\algorithmicthen}{\textbf{then}} +\newcommand{\algorithmicelse}{\textbf{else}} +\newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif} +\newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif} +\newcommand{\algorithmicfor}{\textbf{for}} +\newcommand{\algorithmicforall}{\textbf{for all}} +\newcommand{\algorithmicdo}{\textbf{do}} +\newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor} +\newcommand{\algorithmicwhile}{\textbf{while}} +\newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile} +\newcommand{\algorithmicloop}{\textbf{loop}} +\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop} +\newcommand{\algorithmicrepeat}{\textbf{repeat}} +\newcommand{\algorithmicuntil}{\textbf{until}} + +%changed by alex smola +\newcommand{\algorithmicinput}{\textbf{input}} +\newcommand{\algorithmicoutput}{\textbf{output}} +\newcommand{\algorithmicset}{\textbf{set}} +\newcommand{\algorithmictrue}{\textbf{true}} +\newcommand{\algorithmicfalse}{\textbf{false}} +\newcommand{\algorithmicand}{\textbf{and\ }} +\newcommand{\algorithmicor}{\textbf{or\ }} +\newcommand{\algorithmicfunction}{\textbf{function}} +\newcommand{\algorithmicendfunction}{\algorithmicend\ \algorithmicfunction} +\newcommand{\algorithmicmain}{\textbf{main}} +\newcommand{\algorithmicendmain}{\algorithmicend\ \algorithmicmain} +%end changed by alex smola + +\def\ALC@item[#1]{% +\if@noparitem \@donoparitem + \else \if@inlabel \indent \par \fi + \ifhmode \unskip\unskip \par \fi + \if@newlist \if@nobreak \@nbitem \else + \addpenalty\@beginparpenalty + \addvspace\@topsep \addvspace{-\parskip}\fi + \else \addpenalty\@itempenalty \addvspace\itemsep + \fi + \global\@inlabeltrue +\fi +\everypar{\global\@minipagefalse\global\@newlistfalse + \if@inlabel\global\@inlabelfalse \hskip -\parindent \box\@labels + \penalty\z@ \fi + \everypar{}}\global\@nobreakfalse +\if@noitemarg \@noitemargfalse \if@nmbrlist \refstepcounter{\@listctr}\fi \fi +\sbox\@tempboxa{\makelabel{#1}}% +\global\setbox\@labels + \hbox{\unhbox\@labels \hskip \itemindent + \hskip -\labelwidth \hskip -\ALC@tlm + \ifdim \wd\@tempboxa >\labelwidth + \box\@tempboxa + \else \hbox to\labelwidth {\unhbox\@tempboxa}\fi + \hskip \ALC@tlm}\ignorespaces} +% +\newenvironment{algorithmic}[1][0]{ +\let\@item\ALC@item + \newcommand{\ALC@lno}{% +\ifthenelse{\equal{\arabic{ALC@rem}}{0}} +{{\footnotesize \arabic{ALC@line}:}}{}% +} +\let\@listii\@listi +\let\@listiii\@listi +\let\@listiv\@listi +\let\@listv\@listi +\let\@listvi\@listi +\let\@listvii\@listi + \newenvironment{ALC@g}{ + \begin{list}{\ALC@lno}{ \itemsep\z@ \itemindent\z@ + \listparindent\z@ \rightmargin\z@ + \topsep\z@ \partopsep\z@ \parskip\z@\parsep\z@ + \leftmargin 1em + \addtolength{\ALC@tlm}{\leftmargin} + } + } + {\end{list}} + \newcommand{\ALC@it}{\addtocounter{ALC@line}{1}\addtocounter{ALC@rem}{1}\ifthenelse{\equal{\arabic{ALC@rem}}{#1}}{\setcounter{ALC@rem}{0}}{}\item} + \newcommand{\ALC@com}[1]{\ifthenelse{\equal{##1}{default}}% +{}{\ \algorithmiccomment{##1}}} + \newcommand{\REQUIRE}{\item[\algorithmicrequire]} + \newcommand{\ENSURE}{\item[\algorithmicensure]} + \newcommand{\STATE}{\ALC@it} + \newcommand{\COMMENT}[1]{\algorithmiccomment{##1}} +%changes by alex smola + \newcommand{\INPUT}{\item[\algorithmicinput]} + \newcommand{\OUTPUT}{\item[\algorithmicoutput]} + \newcommand{\SET}{\item[\algorithmicset]} +% \newcommand{\TRUE}{\algorithmictrue} +% \newcommand{\FALSE}{\algorithmicfalse} + \newcommand{\AND}{\algorithmicand} + \newcommand{\OR}{\algorithmicor} + \newenvironment{ALC@func}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@main}{\begin{ALC@g}}{\end{ALC@g}} +%end changes by alex smola + \newenvironment{ALC@if}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@for}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@whl}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@loop}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@rpt}{\begin{ALC@g}}{\end{ALC@g}} + \renewcommand{\\}{\@centercr} + \newcommand{\IF}[2][default]{\ALC@it\algorithmicif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\SHORTIF}[2]{\ALC@it\algorithmicif\ ##1\ + \algorithmicthen\ {##2}} + \newcommand{\ELSE}[1][default]{\end{ALC@if}\ALC@it\algorithmicelse% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSIF}[2][default]% +{\end{ALC@if}\ALC@it\algorithmicelsif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\FOR}[2][default]{\ALC@it\algorithmicfor\ ##2\ \algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\FORALL}[2][default]{\ALC@it\algorithmicforall\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\SHORTFORALL}[2]{\ALC@it\algorithmicforall\ ##1\ % + \algorithmicdo\ {##2}} + \newcommand{\WHILE}[2][default]{\ALC@it\algorithmicwhile\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@whl}} + \newcommand{\LOOP}[1][default]{\ALC@it\algorithmicloop% +\ALC@com{##1}\begin{ALC@loop}} +%changed by alex smola + \newcommand{\FUNCTION}[2][default]{\ALC@it\algorithmicfunction\ ##2\ % + \ALC@com{##1}\begin{ALC@func}} + \newcommand{\MAIN}[2][default]{\ALC@it\algorithmicmain\ ##2\ % + \ALC@com{##1}\begin{ALC@main}} +%end changed by alex smola + \newcommand{\REPEAT}[1][default]{\ALC@it\algorithmicrepeat% + \ALC@com{##1}\begin{ALC@rpt}} + \newcommand{\UNTIL}[1]{\end{ALC@rpt}\ALC@it\algorithmicuntil\ ##1} + \ifthenelse{\boolean{ALC@noend}}{ + \newcommand{\ENDIF}{\end{ALC@if}} + \newcommand{\ENDFOR}{\end{ALC@for}} + \newcommand{\ENDWHILE}{\end{ALC@whl}} + \newcommand{\ENDLOOP}{\end{ALC@loop}} + \newcommand{\ENDFUNCTION}{\end{ALC@func}} + \newcommand{\ENDMAIN}{\end{ALC@main}} + }{ + \newcommand{\ENDIF}{\end{ALC@if}\ALC@it\algorithmicendif} + \newcommand{\ENDFOR}{\end{ALC@for}\ALC@it\algorithmicendfor} + \newcommand{\ENDWHILE}{\end{ALC@whl}\ALC@it\algorithmicendwhile} + \newcommand{\ENDLOOP}{\end{ALC@loop}\ALC@it\algorithmicendloop} + \newcommand{\ENDFUNCTION}{\end{ALC@func}\ALC@it\algorithmicendfunction} + \newcommand{\ENDMAIN}{\end{ALC@main}\ALC@it\algorithmicendmain} + } + \renewcommand{\@toodeep}{} + \begin{list}{\ALC@lno}{\setcounter{ALC@line}{0}\setcounter{ALC@rem}{0}% + \itemsep\z@ \itemindent\z@ \listparindent\z@% + \partopsep\z@ \parskip\z@ \parsep\z@% + \labelsep 0.5em \topsep 0.2em% + \ifthenelse{\equal{#1}{0}} + {\labelwidth 0.5em } + {\labelwidth 1.2em } + \leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep} + \ALC@tlm\labelsep + } + } + {\end{list}} + + + + + + + + + + + + + + diff --git a/docs/ICML_workshop/icml2023/example_paper.bib b/docs/ICML_workshop/icml2023/example_paper.bib new file mode 100644 index 0000000..a4775b7 --- /dev/null +++ b/docs/ICML_workshop/icml2023/example_paper.bib @@ -0,0 +1,75 @@ +@inproceedings{langley00, + author = {P. Langley}, + title = {Crafting Papers on Machine Learning}, + year = {2000}, + pages = {1207--1216}, + editor = {Pat Langley}, + booktitle = {Proceedings of the 17th International Conference + on Machine Learning (ICML 2000)}, + address = {Stanford, CA}, + publisher = {Morgan Kaufmann} +} + +@TechReport{mitchell80, + author = "T. M. Mitchell", + title = "The Need for Biases in Learning Generalizations", + institution = "Computer Science Department, Rutgers University", + year = "1980", + address = "New Brunswick, MA", +} + +@phdthesis{kearns89, + author = {M. J. Kearns}, + title = {Computational Complexity of Machine Learning}, + school = {Department of Computer Science, Harvard University}, + year = {1989} +} + +@Book{MachineLearningI, + editor = "R. S. Michalski and J. G. Carbonell and T. + M. Mitchell", + title = "Machine Learning: An Artificial Intelligence + Approach, Vol. I", + publisher = "Tioga", + year = "1983", + address = "Palo Alto, CA" +} + +@Book{DudaHart2nd, + author = "R. O. Duda and P. E. Hart and D. G. Stork", + title = "Pattern Classification", + publisher = "John Wiley and Sons", + edition = "2nd", + year = "2000" +} + +@misc{anonymous, + title= {Suppressed for Anonymity}, + author= {Author, N. N.}, + year= {2021} +} + +@InCollection{Newell81, + author = "A. Newell and P. S. Rosenbloom", + title = "Mechanisms of Skill Acquisition and the Law of + Practice", + booktitle = "Cognitive Skills and Their Acquisition", + pages = "1--51", + publisher = "Lawrence Erlbaum Associates, Inc.", + year = "1981", + editor = "J. R. Anderson", + chapter = "1", + address = "Hillsdale, NJ" +} + + +@Article{Samuel59, + author = "A. L. Samuel", + title = "Some Studies in Machine Learning Using the Game of + Checkers", + journal = "IBM Journal of Research and Development", + year = "1959", + volume = "3", + number = "3", + pages = "211--229" +} diff --git a/docs/ICML_workshop/icml2023/example_paper.pdf b/docs/ICML_workshop/icml2023/example_paper.pdf new file mode 100644 index 0000000..52c81d5 Binary files /dev/null and b/docs/ICML_workshop/icml2023/example_paper.pdf differ diff --git a/docs/ICML_workshop/icml2023/example_paper.tex b/docs/ICML_workshop/icml2023/example_paper.tex new file mode 100644 index 0000000..1e25d76 --- /dev/null +++ b/docs/ICML_workshop/icml2023/example_paper.tex @@ -0,0 +1,655 @@ +%%%%%%%% ICML 2023 EXAMPLE LATEX SUBMISSION FILE %%%%%%%%%%%%%%%%% + +\documentclass{article} + +% Recommended, but optional, packages for figures and better typesetting: +\usepackage{microtype} +\usepackage{graphicx} +\usepackage{subfigure} +\usepackage{booktabs} % for professional tables + +% hyperref makes hyperlinks in the resulting PDF. +% If your build breaks (sometimes temporarily if a hyperlink spans a page) +% please comment out the following usepackage line and replace +% \usepackage{icml2023} with \usepackage[nohyperref]{icml2023} above. +\usepackage{hyperref} + + +% Attempt to make hyperref and algorithmic work together better: +\newcommand{\theHalgorithm}{\arabic{algorithm}} + +% Use the following line for the initial blind version submitted for review: +\usepackage{icml2023} + +% If accepted, instead use the following line for the camera-ready submission: +% \usepackage[accepted]{icml2023} + +% For theorems and such +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathtools} +\usepackage{amsthm} + +% if you use cleveref.. +\usepackage[capitalize,noabbrev]{cleveref} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% THEOREMS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\theoremstyle{plain} +\newtheorem{theorem}{Theorem}[section] +\newtheorem{proposition}[theorem]{Proposition} +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{corollary}[theorem]{Corollary} +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{assumption}[theorem]{Assumption} +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} + +% Todonotes is useful during development; simply uncomment the next line +% and comment out the line below the next line to turn off comments +%\usepackage[disable,textsize=tiny]{todonotes} +\usepackage[textsize=tiny]{todonotes} + + +% The \icmltitle you define below is probably too long as a header. +% Therefore, a short form for the running title is supplied here: +\icmltitlerunning{Submission and Formatting Instructions for ICML 2023} + +\begin{document} + +\twocolumn[ +\icmltitle{Submission and Formatting Instructions for \\ + International Conference on Machine Learning (ICML 2023)} + +% It is OKAY to include author information, even for blind +% submissions: the style file will automatically remove it for you +% unless you've provided the [accepted] option to the icml2023 +% package. + +% List of affiliations: The first argument should be a (short) +% identifier you will use later to specify author affiliations +% Academic affiliations should list Department, University, City, Region, Country +% Industry affiliations should list Company, City, Region, Country + +% You can specify symbols, otherwise they are numbered in order. +% Ideally, you should not use this facility. Affiliations will be numbered +% in order of appearance and this is the preferred way. +\icmlsetsymbol{equal}{*} + +\begin{icmlauthorlist} +\icmlauthor{Firstname1 Lastname1}{equal,yyy} +\icmlauthor{Firstname2 Lastname2}{equal,yyy,comp} +\icmlauthor{Firstname3 Lastname3}{comp} +\icmlauthor{Firstname4 Lastname4}{sch} +\icmlauthor{Firstname5 Lastname5}{yyy} +\icmlauthor{Firstname6 Lastname6}{sch,yyy,comp} +\icmlauthor{Firstname7 Lastname7}{comp} +%\icmlauthor{}{sch} +\icmlauthor{Firstname8 Lastname8}{sch} +\icmlauthor{Firstname8 Lastname8}{yyy,comp} +%\icmlauthor{}{sch} +%\icmlauthor{}{sch} +\end{icmlauthorlist} + +\icmlaffiliation{yyy}{Department of XXX, University of YYY, Location, Country} +\icmlaffiliation{comp}{Company Name, Location, Country} +\icmlaffiliation{sch}{School of ZZZ, Institute of WWW, Location, Country} + +\icmlcorrespondingauthor{Firstname1 Lastname1}{first1.last1@xxx.edu} +\icmlcorrespondingauthor{Firstname2 Lastname2}{first2.last2@www.uk} + +% You may provide any keywords that you +% find helpful for describing your paper; these are used to populate +% the "keywords" metadata in the PDF but will not be shown in the document +\icmlkeywords{Machine Learning, ICML} + +\vskip 0.3in +] + +% this must go after the closing bracket ] following \twocolumn[ ... + +% This command actually creates the footnote in the first column +% listing the affiliations and the copyright notice. +% The command takes one argument, which is text to display at the start of the footnote. +% The \icmlEqualContribution command is standard text for equal contribution. +% Remove it (just {}) if you do not need this facility. + +%\printAffiliationsAndNotice{} % leave blank if no need to mention equal contribution +\printAffiliationsAndNotice{\icmlEqualContribution} % otherwise use the standard text. + +\begin{abstract} +This document provides a basic paper template and submission guidelines. +Abstracts must be a single paragraph, ideally between 4--6 sentences long. +Gross violations will trigger corrections at the camera-ready phase. +\end{abstract} + +\section{Electronic Submission} +\label{submission} + +Submission to ICML 2023 will be entirely electronic, via a web site +(not email). Information about the submission process and \LaTeX\ templates +are available on the conference web site at: +\begin{center} +\textbf{\texttt{http://icml.cc/}} +\end{center} + +The guidelines below will be enforced for initial submissions and +camera-ready copies. Here is a brief summary: +\begin{itemize} +\item Submissions must be in PDF\@. +\item \textbf{New to this year}: If your paper has appendices, submit the appendix together with the main body and the references \textbf{as a single file}. Reviewers will not look for appendices as a separate PDF file. So if you submit such an extra file, reviewers will very likely miss it. +\item Page limit: The main body of the paper has to be fitted to 8 pages, excluding references and appendices; the space for the latter two is not limited. For the final version of the paper, authors can add one extra page to the main body. +\item \textbf{Do not include author information or acknowledgements} in your + initial submission. +\item Your paper should be in \textbf{10 point Times font}. +\item Make sure your PDF file only uses Type-1 fonts. +\item Place figure captions \emph{under} the figure (and omit titles from inside + the graphic file itself). Place table captions \emph{over} the table. +\item References must include page numbers whenever possible and be as complete + as possible. Place multiple citations in chronological order. +\item Do not alter the style template; in particular, do not compress the paper + format by reducing the vertical spaces. +\item Keep your abstract brief and self-contained, one paragraph and roughly + 4--6 sentences. Gross violations will require correction at the + camera-ready phase. The title should have content words capitalized. +\end{itemize} + +\subsection{Submitting Papers} + +\textbf{Paper Deadline:} The deadline for paper submission that is +advertised on the conference website is strict. If your full, +anonymized, submission does not reach us on time, it will not be +considered for publication. + +\textbf{Anonymous Submission:} ICML uses double-blind review: no identifying +author information may appear on the title page or in the paper +itself. \cref{author info} gives further details. + +\textbf{Simultaneous Submission:} ICML will not accept any paper which, +at the time of submission, is under review for another conference or +has already been published. This policy also applies to papers that +overlap substantially in technical content with conference papers +under review or previously published. ICML submissions must not be +submitted to other conferences and journals during ICML's review +period. +%Authors may submit to ICML substantially different versions of journal papers +%that are currently under review by the journal, but not yet accepted +%at the time of submission. +Informal publications, such as technical +reports or papers in workshop proceedings which do not appear in +print, do not fall under these restrictions. + +\medskip + +Authors must provide their manuscripts in \textbf{PDF} format. +Furthermore, please make sure that files contain only embedded Type-1 fonts +(e.g.,~using the program \texttt{pdffonts} in linux or using +File/DocumentProperties/Fonts in Acrobat). Other fonts (like Type-3) +might come from graphics files imported into the document. + +Authors using \textbf{Word} must convert their document to PDF\@. Most +of the latest versions of Word have the facility to do this +automatically. Submissions will not be accepted in Word format or any +format other than PDF\@. Really. We're not joking. Don't send Word. + +Those who use \textbf{\LaTeX} should avoid including Type-3 fonts. +Those using \texttt{latex} and \texttt{dvips} may need the following +two commands: + +{\footnotesize +\begin{verbatim} +dvips -Ppdf -tletter -G0 -o paper.ps paper.dvi +ps2pdf paper.ps +\end{verbatim}} +It is a zero following the ``-G'', which tells dvips to use +the config.pdf file. Newer \TeX\ distributions don't always need this +option. + +Using \texttt{pdflatex} rather than \texttt{latex}, often gives better +results. This program avoids the Type-3 font problem, and supports more +advanced features in the \texttt{microtype} package. + +\textbf{Graphics files} should be a reasonable size, and included from +an appropriate format. Use vector formats (.eps/.pdf) for plots, +lossless bitmap formats (.png) for raster graphics with sharp lines, and +jpeg for photo-like images. + +The style file uses the \texttt{hyperref} package to make clickable +links in documents. If this causes problems for you, add +\texttt{nohyperref} as one of the options to the \texttt{icml2023} +usepackage statement. + + +\subsection{Submitting Final Camera-Ready Copy} + +The final versions of papers accepted for publication should follow the +same format and naming convention as initial submissions, except that +author information (names and affiliations) should be given. See +\cref{final author} for formatting instructions. + +The footnote, ``Preliminary work. Under review by the International +Conference on Machine Learning (ICML). Do not distribute.'' must be +modified to ``\textit{Proceedings of the +$\mathit{40}^{th}$ International Conference on Machine Learning}, +Honolulu, Hawaii, USA, PMLR 202, 2023. +Copyright 2023 by the author(s).'' + +For those using the \textbf{\LaTeX} style file, this change (and others) is +handled automatically by simply changing +$\mathtt{\backslash usepackage\{icml2023\}}$ to +$$\mathtt{\backslash usepackage[accepted]\{icml2023\}}$$ +Authors using \textbf{Word} must edit the +footnote on the first page of the document themselves. + +Camera-ready copies should have the title of the paper as running head +on each page except the first one. The running title consists of a +single line centered above a horizontal rule which is $1$~point thick. +The running head should be centered, bold and in $9$~point type. The +rule should be $10$~points above the main text. For those using the +\textbf{\LaTeX} style file, the original title is automatically set as running +head using the \texttt{fancyhdr} package which is included in the ICML +2023 style file package. In case that the original title exceeds the +size restrictions, a shorter form can be supplied by using + +\verb|\icmltitlerunning{...}| + +just before $\mathtt{\backslash begin\{document\}}$. +Authors using \textbf{Word} must edit the header of the document themselves. + +\section{Format of the Paper} + +All submissions must follow the specified format. + +\subsection{Dimensions} + + + + +The text of the paper should be formatted in two columns, with an +overall width of 6.75~inches, height of 9.0~inches, and 0.25~inches +between the columns. The left margin should be 0.75~inches and the top +margin 1.0~inch (2.54~cm). The right and bottom margins will depend on +whether you print on US letter or A4 paper, but all final versions +must be produced for US letter size. +Do not write anything on the margins. + +The paper body should be set in 10~point type with a vertical spacing +of 11~points. Please use Times typeface throughout the text. + +\subsection{Title} + +The paper title should be set in 14~point bold type and centered +between two horizontal rules that are 1~point thick, with 1.0~inch +between the top rule and the top edge of the page. Capitalize the +first letter of content words and put the rest of the title in lower +case. + +\subsection{Author Information for Submission} +\label{author info} + +ICML uses double-blind review, so author information must not appear. If +you are using \LaTeX\/ and the \texttt{icml2023.sty} file, use +\verb+\icmlauthor{...}+ to specify authors and \verb+\icmlaffiliation{...}+ to specify affiliations. (Read the TeX code used to produce this document for an example usage.) The author information +will not be printed unless \texttt{accepted} is passed as an argument to the +style file. +Submissions that include the author information will not +be reviewed. + +\subsubsection{Self-Citations} + +If you are citing published papers for which you are an author, refer +to yourself in the third person. In particular, do not use phrases +that reveal your identity (e.g., ``in previous work \cite{langley00}, we +have shown \ldots''). + +Do not anonymize citations in the reference section. The only exception are manuscripts that are +not yet published (e.g., under submission). If you choose to refer to +such unpublished manuscripts \cite{anonymous}, anonymized copies have +to be submitted +as Supplementary Material via CMT\@. However, keep in mind that an ICML +paper should be self contained and should contain sufficient detail +for the reviewers to evaluate the work. In particular, reviewers are +not required to look at the Supplementary Material when writing their +review (they are not required to look at more than the first $8$ pages of the submitted document). + +\subsubsection{Camera-Ready Author Information} +\label{final author} + +If a paper is accepted, a final camera-ready copy must be prepared. +% +For camera-ready papers, author information should start 0.3~inches below the +bottom rule surrounding the title. The authors' names should appear in 10~point +bold type, in a row, separated by white space, and centered. Author names should +not be broken across lines. Unbolded superscripted numbers, starting 1, should +be used to refer to affiliations. + +Affiliations should be numbered in the order of appearance. A single footnote +block of text should be used to list all the affiliations. (Academic +affiliations should list Department, University, City, State/Region, Country. +Similarly for industrial affiliations.) + +Each distinct affiliations should be listed once. If an author has multiple +affiliations, multiple superscripts should be placed after the name, separated +by thin spaces. If the authors would like to highlight equal contribution by +multiple first authors, those authors should have an asterisk placed after their +name in superscript, and the term ``\textsuperscript{*}Equal contribution" +should be placed in the footnote block ahead of the list of affiliations. A +list of corresponding authors and their emails (in the format Full Name +\textless{}email@domain.com\textgreater{}) can follow the list of affiliations. +Ideally only one or two names should be listed. + +A sample file with author names is included in the ICML2023 style file +package. Turn on the \texttt{[accepted]} option to the stylefile to +see the names rendered. All of the guidelines above are implemented +by the \LaTeX\ style file. + +\subsection{Abstract} + +The paper abstract should begin in the left column, 0.4~inches below the final +address. The heading `Abstract' should be centered, bold, and in 11~point type. +The abstract body should use 10~point type, with a vertical spacing of +11~points, and should be indented 0.25~inches more than normal on left-hand and +right-hand margins. Insert 0.4~inches of blank space after the body. Keep your +abstract brief and self-contained, limiting it to one paragraph and roughly 4--6 +sentences. Gross violations will require correction at the camera-ready phase. + +\subsection{Partitioning the Text} + +You should organize your paper into sections and paragraphs to help +readers place a structure on the material and understand its +contributions. + +\subsubsection{Sections and Subsections} + +Section headings should be numbered, flush left, and set in 11~pt bold +type with the content words capitalized. Leave 0.25~inches of space +before the heading and 0.15~inches after the heading. + +Similarly, subsection headings should be numbered, flush left, and set +in 10~pt bold type with the content words capitalized. Leave +0.2~inches of space before the heading and 0.13~inches afterward. + +Finally, subsubsection headings should be numbered, flush left, and +set in 10~pt small caps with the content words capitalized. Leave +0.18~inches of space before the heading and 0.1~inches after the +heading. + +Please use no more than three levels of headings. + +\subsubsection{Paragraphs and Footnotes} + +Within each section or subsection, you should further partition the +paper into paragraphs. Do not indent the first line of a given +paragraph, but insert a blank line between succeeding ones. + +You can use footnotes\footnote{Footnotes +should be complete sentences.} to provide readers with additional +information about a topic without interrupting the flow of the paper. +Indicate footnotes with a number in the text where the point is most +relevant. Place the footnote in 9~point type at the bottom of the +column in which it appears. Precede the first footnote in a column +with a horizontal rule of 0.8~inches.\footnote{Multiple footnotes can +appear in each column, in the same order as they appear in the text, +but spread them across columns and pages if possible.} + +\begin{figure}[ht] +\vskip 0.2in +\begin{center} +\centerline{\includegraphics[width=\columnwidth]{icml_numpapers}} +\caption{Historical locations and number of accepted papers for International +Machine Learning Conferences (ICML 1993 -- ICML 2008) and International +Workshops on Machine Learning (ML 1988 -- ML 1992). At the time this figure was +produced, the number of accepted papers for ICML 2008 was unknown and instead +estimated.} +\label{icml-historical} +\end{center} +\vskip -0.2in +\end{figure} + +\subsection{Figures} + +You may want to include figures in the paper to illustrate +your approach and results. Such artwork should be centered, +legible, and separated from the text. Lines should be dark and at +least 0.5~points thick for purposes of reproduction, and text should +not appear on a gray background. + +Label all distinct components of each figure. If the figure takes the +form of a graph, then give a name for each axis and include a legend +that briefly describes each curve. Do not include a title inside the +figure; instead, the caption should serve this function. + +Number figures sequentially, placing the figure number and caption +\emph{after} the graphics, with at least 0.1~inches of space before +the caption and 0.1~inches after it, as in +\cref{icml-historical}. The figure caption should be set in +9~point type and centered unless it runs two or more lines, in which +case it should be flush left. You may float figures to the top or +bottom of a column, and you may set wide figures across both columns +(use the environment \texttt{figure*} in \LaTeX). Always place +two-column figures at the top or bottom of the page. + +\subsection{Algorithms} + +If you are using \LaTeX, please use the ``algorithm'' and ``algorithmic'' +environments to format pseudocode. These require +the corresponding stylefiles, algorithm.sty and +algorithmic.sty, which are supplied with this package. +\cref{alg:example} shows an example. + +\begin{algorithm}[tb] + \caption{Bubble Sort} + \label{alg:example} +\begin{algorithmic} + \STATE {\bfseries Input:} data $x_i$, size $m$ + \REPEAT + \STATE Initialize $noChange = true$. + \FOR{$i=1$ {\bfseries to} $m-1$} + \IF{$x_i > x_{i+1}$} + \STATE Swap $x_i$ and $x_{i+1}$ + \STATE $noChange = false$ + \ENDIF + \ENDFOR + \UNTIL{$noChange$ is $true$} +\end{algorithmic} +\end{algorithm} + +\subsection{Tables} + +You may also want to include tables that summarize material. Like +figures, these should be centered, legible, and numbered consecutively. +However, place the title \emph{above} the table with at least +0.1~inches of space before the title and the same after it, as in +\cref{sample-table}. The table title should be set in 9~point +type and centered unless it runs two or more lines, in which case it +should be flush left. + +% Note use of \abovespace and \belowspace to get reasonable spacing +% above and below tabular lines. + +\begin{table}[t] +\caption{Classification accuracies for naive Bayes and flexible +Bayes on various data sets.} +\label{sample-table} +\vskip 0.15in +\begin{center} +\begin{small} +\begin{sc} +\begin{tabular}{lcccr} +\toprule +Data set & Naive & Flexible & Better? \\ +\midrule +Breast & 95.9$\pm$ 0.2& 96.7$\pm$ 0.2& $\surd$ \\ +Cleveland & 83.3$\pm$ 0.6& 80.0$\pm$ 0.6& $\times$\\ +Glass2 & 61.9$\pm$ 1.4& 83.8$\pm$ 0.7& $\surd$ \\ +Credit & 74.8$\pm$ 0.5& 78.3$\pm$ 0.6& \\ +Horse & 73.3$\pm$ 0.9& 69.7$\pm$ 1.0& $\times$\\ +Meta & 67.1$\pm$ 0.6& 76.5$\pm$ 0.5& $\surd$ \\ +Pima & 75.1$\pm$ 0.6& 73.9$\pm$ 0.5& \\ +Vehicle & 44.9$\pm$ 0.6& 61.5$\pm$ 0.4& $\surd$ \\ +\bottomrule +\end{tabular} +\end{sc} +\end{small} +\end{center} +\vskip -0.1in +\end{table} + +Tables contain textual material, whereas figures contain graphical material. +Specify the contents of each row and column in the table's topmost +row. Again, you may float tables to a column's top or bottom, and set +wide tables across both columns. Place two-column tables at the +top or bottom of the page. + +\subsection{Theorems and such} +The preferred way is to number definitions, propositions, lemmas, etc. consecutively, within sections, as shown below. +\begin{definition} +\label{def:inj} +A function $f:X \to Y$ is injective if for any $x,y\in X$ different, $f(x)\ne f(y)$. +\end{definition} +Using \cref{def:inj} we immediate get the following result: +\begin{proposition} +If $f$ is injective mapping a set $X$ to another set $Y$, +the cardinality of $Y$ is at least as large as that of $X$ +\end{proposition} +\begin{proof} +Left as an exercise to the reader. +\end{proof} +\cref{lem:usefullemma} stated next will prove to be useful. +\begin{lemma} +\label{lem:usefullemma} +For any $f:X \to Y$ and $g:Y\to Z$ injective functions, $f \circ g$ is injective. +\end{lemma} +\begin{theorem} +\label{thm:bigtheorem} +If $f:X\to Y$ is bijective, the cardinality of $X$ and $Y$ are the same. +\end{theorem} +An easy corollary of \cref{thm:bigtheorem} is the following: +\begin{corollary} +If $f:X\to Y$ is bijective, +the cardinality of $X$ is at least as large as that of $Y$. +\end{corollary} +\begin{assumption} +The set $X$ is finite. +\label{ass:xfinite} +\end{assumption} +\begin{remark} +According to some, it is only the finite case (cf. \cref{ass:xfinite}) that is interesting. +\end{remark} +%restatable + +\subsection{Citations and References} + +Please use APA reference format regardless of your formatter +or word processor. If you rely on the \LaTeX\/ bibliographic +facility, use \texttt{natbib.sty} and \texttt{icml2023.bst} +included in the style-file package to obtain this format. + +Citations within the text should include the authors' last names and +year. If the authors' names are included in the sentence, place only +the year in parentheses, for example when referencing Arthur Samuel's +pioneering work \yrcite{Samuel59}. Otherwise place the entire +reference in parentheses with the authors and year separated by a +comma \cite{Samuel59}. List multiple references separated by +semicolons \cite{kearns89,Samuel59,mitchell80}. Use the `et~al.' +construct only for citations with three or more authors or after +listing all authors to a publication in an earlier reference \cite{MachineLearningI}. + +Authors should cite their own work in the third person +in the initial version of their paper submitted for blind review. +Please refer to \cref{author info} for detailed instructions on how to +cite your own papers. + +Use an unnumbered first-level section heading for the references, and use a +hanging indent style, with the first line of the reference flush against the +left margin and subsequent lines indented by 10 points. The references at the +end of this document give examples for journal articles \cite{Samuel59}, +conference publications \cite{langley00}, book chapters \cite{Newell81}, books +\cite{DudaHart2nd}, edited volumes \cite{MachineLearningI}, technical reports +\cite{mitchell80}, and dissertations \cite{kearns89}. + +Alphabetize references by the surnames of the first authors, with +single author entries preceding multiple author entries. Order +references for the same authors by year of publication, with the +earliest first. Make sure that each reference includes all relevant +information (e.g., page numbers). + +Please put some effort into making references complete, presentable, and +consistent, e.g. use the actual current name of authors. +If using bibtex, please protect capital letters of names and +abbreviations in titles, for example, use \{B\}ayesian or \{L\}ipschitz +in your .bib file. + +\section*{Accessibility} +Authors are kindly asked to make their submissions as accessible as possible for everyone including people with disabilities and sensory or neurological differences. +Tips of how to achieve this and what to pay attention to will be provided on the conference website \url{http://icml.cc/}. + +\section*{Software and Data} + +If a paper is accepted, we strongly encourage the publication of software and data with the +camera-ready version of the paper whenever appropriate. This can be +done by including a URL in the camera-ready copy. However, \textbf{do not} +include URLs that reveal your institution or identity in your +submission for review. Instead, provide an anonymous URL or upload +the material as ``Supplementary Material'' into the CMT reviewing +system. Note that reviewers are not required to look at this material +when writing their review. + +% Acknowledgements should only appear in the accepted version. +\section*{Acknowledgements} + +\textbf{Do not} include acknowledgements in the initial version of +the paper submitted for blind review. + +If a paper is accepted, the final camera-ready version can (and +probably should) include acknowledgements. In this case, please +place such acknowledgements in an unnumbered section at the +end of the paper. Typically, this will include thanks to reviewers +who gave useful comments, to colleagues who contributed to the ideas, +and to funding agencies and corporate sponsors that provided financial +support. + + +% In the unusual situation where you want a paper to appear in the +% references without citing it in the main text, use \nocite +\nocite{langley00} + +\bibliography{example_paper} +\bibliographystyle{icml2023} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% APPENDIX +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newpage +\appendix +\onecolumn +\section{You \emph{can} have an appendix here.} + +You can have as much text here as you want. The main body must be at most $8$ pages long. +For the final version, one more page can be added. +If you want, you can use an appendix like this one, even using the one-column format. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\end{document} + + +% This document was modified from the file originally made available by +% Pat Langley and Andrea Danyluk for ICML-2K. This version was created +% by Iain Murray in 2018, and modified by Alexandre Bouchard in +% 2019 and 2021 and by Csaba Szepesvari, Gang Niu and Sivan Sabato in 2022. +% Modified again in 2023 by Sivan Sabato and Jonathan Scarlett. +% Previous contributors include Dan Roy, Lise Getoor and Tobias +% Scheffer, which was slightly modified from the 2010 version by +% Thorsten Joachims & Johannes Fuernkranz, slightly modified from the +% 2009 version by Kiri Wagstaff and Sam Roweis's 2008 version, which is +% slightly modified from Prasad Tadepalli's 2007 version which is a +% lightly changed version of the previous year's version by Andrew +% Moore, which was in turn edited from those of Kristian Kersting and +% Codrina Lauth. Alex Smola contributed to the algorithmic style files. diff --git a/docs/ICML_workshop/icml2023/fancyhdr.sty b/docs/ICML_workshop/icml2023/fancyhdr.sty new file mode 100644 index 0000000..5a4d897 --- /dev/null +++ b/docs/ICML_workshop/icml2023/fancyhdr.sty @@ -0,0 +1,485 @@ +% fancyhdr.sty version 3.2 +% Fancy headers and footers for LaTeX. +% Piet van Oostrum, +% Dept of Computer and Information Sciences, University of Utrecht, +% Padualaan 14, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands +% Telephone: +31 30 2532180. Email: piet@cs.uu.nl +% ======================================================================== +% LICENCE: +% This file may be distributed under the terms of the LaTeX Project Public +% License, as described in lppl.txt in the base LaTeX distribution. +% Either version 1 or, at your option, any later version. +% ======================================================================== +% MODIFICATION HISTORY: +% Sep 16, 1994 +% version 1.4: Correction for use with \reversemargin +% Sep 29, 1994: +% version 1.5: Added the \iftopfloat, \ifbotfloat and \iffloatpage commands +% Oct 4, 1994: +% version 1.6: Reset single spacing in headers/footers for use with +% setspace.sty or doublespace.sty +% Oct 4, 1994: +% version 1.7: changed \let\@mkboth\markboth to +% \def\@mkboth{\protect\markboth} to make it more robust +% Dec 5, 1994: +% version 1.8: corrections for amsbook/amsart: define \@chapapp and (more +% importantly) use the \chapter/sectionmark definitions from ps@headings if +% they exist (which should be true for all standard classes). +% May 31, 1995: +% version 1.9: The proposed \renewcommand{\headrulewidth}{\iffloatpage... +% construction in the doc did not work properly with the fancyplain style. +% June 1, 1995: +% version 1.91: The definition of \@mkboth wasn't restored on subsequent +% \pagestyle{fancy}'s. +% June 1, 1995: +% version 1.92: The sequence \pagestyle{fancyplain} \pagestyle{plain} +% \pagestyle{fancy} would erroneously select the plain version. +% June 1, 1995: +% version 1.93: \fancypagestyle command added. +% Dec 11, 1995: +% version 1.94: suggested by Conrad Hughes +% CJCH, Dec 11, 1995: added \footruleskip to allow control over footrule +% position (old hardcoded value of .3\normalbaselineskip is far too high +% when used with very small footer fonts). +% Jan 31, 1996: +% version 1.95: call \@normalsize in the reset code if that is defined, +% otherwise \normalsize. +% this is to solve a problem with ucthesis.cls, as this doesn't +% define \@currsize. Unfortunately for latex209 calling \normalsize doesn't +% work as this is optimized to do very little, so there \@normalsize should +% be called. Hopefully this code works for all versions of LaTeX known to +% mankind. +% April 25, 1996: +% version 1.96: initialize \headwidth to a magic (negative) value to catch +% most common cases that people change it before calling \pagestyle{fancy}. +% Note it can't be initialized when reading in this file, because +% \textwidth could be changed afterwards. This is quite probable. +% We also switch to \MakeUppercase rather than \uppercase and introduce a +% \nouppercase command for use in headers. and footers. +% May 3, 1996: +% version 1.97: Two changes: +% 1. Undo the change in version 1.8 (using the pagestyle{headings} defaults +% for the chapter and section marks. The current version of amsbook and +% amsart classes don't seem to need them anymore. Moreover the standard +% latex classes don't use \markboth if twoside isn't selected, and this is +% confusing as \leftmark doesn't work as expected. +% 2. include a call to \ps@empty in ps@@fancy. This is to solve a problem +% in the amsbook and amsart classes, that make global changes to \topskip, +% which are reset in \ps@empty. Hopefully this doesn't break other things. +% May 7, 1996: +% version 1.98: +% Added % after the line \def\nouppercase +% May 7, 1996: +% version 1.99: This is the alpha version of fancyhdr 2.0 +% Introduced the new commands \fancyhead, \fancyfoot, and \fancyhf. +% Changed \headrulewidth, \footrulewidth, \footruleskip to +% macros rather than length parameters, In this way they can be +% conditionalized and they don't consume length registers. There is no need +% to have them as length registers unless you want to do calculations with +% them, which is unlikely. Note that this may make some uses of them +% incompatible (i.e. if you have a file that uses \setlength or \xxxx=) +% May 10, 1996: +% version 1.99a: +% Added a few more % signs +% May 10, 1996: +% version 1.99b: +% Changed the syntax of \f@nfor to be resistent to catcode changes of := +% Removed the [1] from the defs of \lhead etc. because the parameter is +% consumed by the \@[xy]lhead etc. macros. +% June 24, 1997: +% version 1.99c: +% corrected \nouppercase to also include the protected form of \MakeUppercase +% \global added to manipulation of \headwidth. +% \iffootnote command added. +% Some comments added about \@fancyhead and \@fancyfoot. +% Aug 24, 1998 +% version 1.99d +% Changed the default \ps@empty to \ps@@empty in order to allow +% \fancypagestyle{empty} redefinition. +% Oct 11, 2000 +% version 2.0 +% Added LPPL license clause. +% +% A check for \headheight is added. An errormessage is given (once) if the +% header is too large. Empty headers don't generate the error even if +% \headheight is very small or even 0pt. +% Warning added for the use of 'E' option when twoside option is not used. +% In this case the 'E' fields will never be used. +% +% Mar 10, 2002 +% version 2.1beta +% New command: \fancyhfoffset[place]{length} +% defines offsets to be applied to the header/footer to let it stick into +% the margins (if length > 0). +% place is like in fancyhead, except that only E,O,L,R can be used. +% This replaces the old calculation based on \headwidth and the marginpar +% area. +% \headwidth will be dynamically calculated in the headers/footers when +% this is used. +% +% Mar 26, 2002 +% version 2.1beta2 +% \fancyhfoffset now also takes h,f as possible letters in the argument to +% allow the header and footer widths to be different. +% New commands \fancyheadoffset and \fancyfootoffset added comparable to +% \fancyhead and \fancyfoot. +% Errormessages and warnings have been made more informative. +% +% Dec 9, 2002 +% version 2.1 +% The defaults for \footrulewidth, \plainheadrulewidth and +% \plainfootrulewidth are changed from \z@skip to 0pt. In this way when +% someone inadvertantly uses \setlength to change any of these, the value +% of \z@skip will not be changed, rather an errormessage will be given. + +% March 3, 2004 +% Release of version 3.0 + +% Oct 7, 2004 +% version 3.1 +% Added '\endlinechar=13' to \fancy@reset to prevent problems with +% includegraphics in header when verbatiminput is active. + +% March 22, 2005 +% version 3.2 +% reset \everypar (the real one) in \fancy@reset because spanish.ldf does +% strange things with \everypar between << and >>. + +\def\ifancy@mpty#1{\def\temp@a{#1}\ifx\temp@a\@empty} + +\def\fancy@def#1#2{\ifancy@mpty{#2}\fancy@gbl\def#1{\leavevmode}\else + \fancy@gbl\def#1{#2\strut}\fi} + +\let\fancy@gbl\global + +\def\@fancyerrmsg#1{% + \ifx\PackageError\undefined + \errmessage{#1}\else + \PackageError{Fancyhdr}{#1}{}\fi} +\def\@fancywarning#1{% + \ifx\PackageWarning\undefined + \errmessage{#1}\else + \PackageWarning{Fancyhdr}{#1}{}\fi} + +% Usage: \@forc \var{charstring}{command to be executed for each char} +% This is similar to LaTeX's \@tfor, but expands the charstring. + +\def\@forc#1#2#3{\expandafter\f@rc\expandafter#1\expandafter{#2}{#3}} +\def\f@rc#1#2#3{\def\temp@ty{#2}\ifx\@empty\temp@ty\else + \f@@rc#1#2\f@@rc{#3}\fi} +\def\f@@rc#1#2#3\f@@rc#4{\def#1{#2}#4\f@rc#1{#3}{#4}} + +% Usage: \f@nfor\name:=list\do{body} +% Like LaTeX's \@for but an empty list is treated as a list with an empty +% element + +\newcommand{\f@nfor}[3]{\edef\@fortmp{#2}% + \expandafter\@forloop#2,\@nil,\@nil\@@#1{#3}} + +% Usage: \def@ult \cs{defaults}{argument} +% sets \cs to the characters from defaults appearing in argument +% or defaults if it would be empty. All characters are lowercased. + +\newcommand\def@ult[3]{% + \edef\temp@a{\lowercase{\edef\noexpand\temp@a{#3}}}\temp@a + \def#1{}% + \@forc\tmpf@ra{#2}% + {\expandafter\if@in\tmpf@ra\temp@a{\edef#1{#1\tmpf@ra}}{}}% + \ifx\@empty#1\def#1{#2}\fi} +% +% \if@in +% +\newcommand{\if@in}[4]{% + \edef\temp@a{#2}\def\temp@b##1#1##2\temp@b{\def\temp@b{##1}}% + \expandafter\temp@b#2#1\temp@b\ifx\temp@a\temp@b #4\else #3\fi} + +\newcommand{\fancyhead}{\@ifnextchar[{\f@ncyhf\fancyhead h}% + {\f@ncyhf\fancyhead h[]}} +\newcommand{\fancyfoot}{\@ifnextchar[{\f@ncyhf\fancyfoot f}% + {\f@ncyhf\fancyfoot f[]}} +\newcommand{\fancyhf}{\@ifnextchar[{\f@ncyhf\fancyhf{}}% + {\f@ncyhf\fancyhf{}[]}} + +% New commands for offsets added + +\newcommand{\fancyheadoffset}{\@ifnextchar[{\f@ncyhfoffs\fancyheadoffset h}% + {\f@ncyhfoffs\fancyheadoffset h[]}} +\newcommand{\fancyfootoffset}{\@ifnextchar[{\f@ncyhfoffs\fancyfootoffset f}% + {\f@ncyhfoffs\fancyfootoffset f[]}} +\newcommand{\fancyhfoffset}{\@ifnextchar[{\f@ncyhfoffs\fancyhfoffset{}}% + {\f@ncyhfoffs\fancyhfoffset{}[]}} + +% The header and footer fields are stored in command sequences with +% names of the form: \f@ncy with for [eo], from [lcr] +% and from [hf]. + +\def\f@ncyhf#1#2[#3]#4{% + \def\temp@c{}% + \@forc\tmpf@ra{#3}% + {\expandafter\if@in\tmpf@ra{eolcrhf,EOLCRHF}% + {}{\edef\temp@c{\temp@c\tmpf@ra}}}% + \ifx\@empty\temp@c\else + \@fancyerrmsg{Illegal char `\temp@c' in \string#1 argument: + [#3]}% + \fi + \f@nfor\temp@c{#3}% + {\def@ult\f@@@eo{eo}\temp@c + \if@twoside\else + \if\f@@@eo e\@fancywarning + {\string#1's `E' option without twoside option is useless}\fi\fi + \def@ult\f@@@lcr{lcr}\temp@c + \def@ult\f@@@hf{hf}{#2\temp@c}% + \@forc\f@@eo\f@@@eo + {\@forc\f@@lcr\f@@@lcr + {\@forc\f@@hf\f@@@hf + {\expandafter\fancy@def\csname + f@ncy\f@@eo\f@@lcr\f@@hf\endcsname + {#4}}}}}} + +\def\f@ncyhfoffs#1#2[#3]#4{% + \def\temp@c{}% + \@forc\tmpf@ra{#3}% + {\expandafter\if@in\tmpf@ra{eolrhf,EOLRHF}% + {}{\edef\temp@c{\temp@c\tmpf@ra}}}% + \ifx\@empty\temp@c\else + \@fancyerrmsg{Illegal char `\temp@c' in \string#1 argument: + [#3]}% + \fi + \f@nfor\temp@c{#3}% + {\def@ult\f@@@eo{eo}\temp@c + \if@twoside\else + \if\f@@@eo e\@fancywarning + {\string#1's `E' option without twoside option is useless}\fi\fi + \def@ult\f@@@lcr{lr}\temp@c + \def@ult\f@@@hf{hf}{#2\temp@c}% + \@forc\f@@eo\f@@@eo + {\@forc\f@@lcr\f@@@lcr + {\@forc\f@@hf\f@@@hf + {\expandafter\setlength\csname + f@ncyO@\f@@eo\f@@lcr\f@@hf\endcsname + {#4}}}}}% + \fancy@setoffs} + +% Fancyheadings version 1 commands. These are more or less deprecated, +% but they continue to work. + +\newcommand{\lhead}{\@ifnextchar[{\@xlhead}{\@ylhead}} +\def\@xlhead[#1]#2{\fancy@def\f@ncyelh{#1}\fancy@def\f@ncyolh{#2}} +\def\@ylhead#1{\fancy@def\f@ncyelh{#1}\fancy@def\f@ncyolh{#1}} + +\newcommand{\chead}{\@ifnextchar[{\@xchead}{\@ychead}} +\def\@xchead[#1]#2{\fancy@def\f@ncyech{#1}\fancy@def\f@ncyoch{#2}} +\def\@ychead#1{\fancy@def\f@ncyech{#1}\fancy@def\f@ncyoch{#1}} + +\newcommand{\rhead}{\@ifnextchar[{\@xrhead}{\@yrhead}} +\def\@xrhead[#1]#2{\fancy@def\f@ncyerh{#1}\fancy@def\f@ncyorh{#2}} +\def\@yrhead#1{\fancy@def\f@ncyerh{#1}\fancy@def\f@ncyorh{#1}} + +\newcommand{\lfoot}{\@ifnextchar[{\@xlfoot}{\@ylfoot}} +\def\@xlfoot[#1]#2{\fancy@def\f@ncyelf{#1}\fancy@def\f@ncyolf{#2}} +\def\@ylfoot#1{\fancy@def\f@ncyelf{#1}\fancy@def\f@ncyolf{#1}} + +\newcommand{\cfoot}{\@ifnextchar[{\@xcfoot}{\@ycfoot}} +\def\@xcfoot[#1]#2{\fancy@def\f@ncyecf{#1}\fancy@def\f@ncyocf{#2}} +\def\@ycfoot#1{\fancy@def\f@ncyecf{#1}\fancy@def\f@ncyocf{#1}} + +\newcommand{\rfoot}{\@ifnextchar[{\@xrfoot}{\@yrfoot}} +\def\@xrfoot[#1]#2{\fancy@def\f@ncyerf{#1}\fancy@def\f@ncyorf{#2}} +\def\@yrfoot#1{\fancy@def\f@ncyerf{#1}\fancy@def\f@ncyorf{#1}} + +\newlength{\fancy@headwidth} +\let\headwidth\fancy@headwidth +\newlength{\f@ncyO@elh} +\newlength{\f@ncyO@erh} +\newlength{\f@ncyO@olh} +\newlength{\f@ncyO@orh} +\newlength{\f@ncyO@elf} +\newlength{\f@ncyO@erf} +\newlength{\f@ncyO@olf} +\newlength{\f@ncyO@orf} +\newcommand{\headrulewidth}{0.4pt} +\newcommand{\footrulewidth}{0pt} +\newcommand{\footruleskip}{.3\normalbaselineskip} + +% Fancyplain stuff shouldn't be used anymore (rather +% \fancypagestyle{plain} should be used), but it must be present for +% compatibility reasons. + +\newcommand{\plainheadrulewidth}{0pt} +\newcommand{\plainfootrulewidth}{0pt} +\newif\if@fancyplain \@fancyplainfalse +\def\fancyplain#1#2{\if@fancyplain#1\else#2\fi} + +\headwidth=-123456789sp %magic constant + +% Command to reset various things in the headers: +% a.o. single spacing (taken from setspace.sty) +% and the catcode of ^^M (so that epsf files in the header work if a +% verbatim crosses a page boundary) +% It also defines a \nouppercase command that disables \uppercase and +% \Makeuppercase. It can only be used in the headers and footers. +\let\fnch@everypar\everypar% save real \everypar because of spanish.ldf +\def\fancy@reset{\fnch@everypar{}\restorecr\endlinechar=13 + \def\baselinestretch{1}% + \def\nouppercase##1{{\let\uppercase\relax\let\MakeUppercase\relax + \expandafter\let\csname MakeUppercase \endcsname\relax##1}}% + \ifx\undefined\@newbaseline% NFSS not present; 2.09 or 2e + \ifx\@normalsize\undefined \normalsize % for ucthesis.cls + \else \@normalsize \fi + \else% NFSS (2.09) present + \@newbaseline% + \fi} + +% Initialization of the head and foot text. + +% The default values still contain \fancyplain for compatibility. +\fancyhf{} % clear all +% lefthead empty on ``plain'' pages, \rightmark on even, \leftmark on odd pages +% evenhead empty on ``plain'' pages, \leftmark on even, \rightmark on odd pages +\if@twoside + \fancyhead[el,or]{\fancyplain{}{\sl\rightmark}} + \fancyhead[er,ol]{\fancyplain{}{\sl\leftmark}} +\else + \fancyhead[l]{\fancyplain{}{\sl\rightmark}} + \fancyhead[r]{\fancyplain{}{\sl\leftmark}} +\fi +\fancyfoot[c]{\rm\thepage} % page number + +% Use box 0 as a temp box and dimen 0 as temp dimen. +% This can be done, because this code will always +% be used inside another box, and therefore the changes are local. + +\def\@fancyvbox#1#2{\setbox0\vbox{#2}\ifdim\ht0>#1\@fancywarning + {\string#1 is too small (\the#1): ^^J Make it at least \the\ht0.^^J + We now make it that large for the rest of the document.^^J + This may cause the page layout to be inconsistent, however\@gobble}% + \dimen0=#1\global\setlength{#1}{\ht0}\ht0=\dimen0\fi + \box0} + +% Put together a header or footer given the left, center and +% right text, fillers at left and right and a rule. +% The \lap commands put the text into an hbox of zero size, +% so overlapping text does not generate an errormessage. +% These macros have 5 parameters: +% 1. LEFTSIDE BEARING % This determines at which side the header will stick +% out. When \fancyhfoffset is used this calculates \headwidth, otherwise +% it is \hss or \relax (after expansion). +% 2. \f@ncyolh, \f@ncyelh, \f@ncyolf or \f@ncyelf. This is the left component. +% 3. \f@ncyoch, \f@ncyech, \f@ncyocf or \f@ncyecf. This is the middle comp. +% 4. \f@ncyorh, \f@ncyerh, \f@ncyorf or \f@ncyerf. This is the right component. +% 5. RIGHTSIDE BEARING. This is always \relax or \hss (after expansion). + +\def\@fancyhead#1#2#3#4#5{#1\hbox to\headwidth{\fancy@reset + \@fancyvbox\headheight{\hbox + {\rlap{\parbox[b]{\headwidth}{\raggedright#2}}\hfill + \parbox[b]{\headwidth}{\centering#3}\hfill + \llap{\parbox[b]{\headwidth}{\raggedleft#4}}}\headrule}}#5} + +\def\@fancyfoot#1#2#3#4#5{#1\hbox to\headwidth{\fancy@reset + \@fancyvbox\footskip{\footrule + \hbox{\rlap{\parbox[t]{\headwidth}{\raggedright#2}}\hfill + \parbox[t]{\headwidth}{\centering#3}\hfill + \llap{\parbox[t]{\headwidth}{\raggedleft#4}}}}}#5} + +\def\headrule{{\if@fancyplain\let\headrulewidth\plainheadrulewidth\fi + \hrule\@height\headrulewidth\@width\headwidth \vskip-\headrulewidth}} + +\def\footrule{{\if@fancyplain\let\footrulewidth\plainfootrulewidth\fi + \vskip-\footruleskip\vskip-\footrulewidth + \hrule\@width\headwidth\@height\footrulewidth\vskip\footruleskip}} + +\def\ps@fancy{% +\@ifundefined{@chapapp}{\let\@chapapp\chaptername}{}%for amsbook +% +% Define \MakeUppercase for old LaTeXen. +% Note: we used \def rather than \let, so that \let\uppercase\relax (from +% the version 1 documentation) will still work. +% +\@ifundefined{MakeUppercase}{\def\MakeUppercase{\uppercase}}{}% +\@ifundefined{chapter}{\def\sectionmark##1{\markboth +{\MakeUppercase{\ifnum \c@secnumdepth>\z@ + \thesection\hskip 1em\relax \fi ##1}}{}}% +\def\subsectionmark##1{\markright {\ifnum \c@secnumdepth >\@ne + \thesubsection\hskip 1em\relax \fi ##1}}}% +{\def\chaptermark##1{\markboth {\MakeUppercase{\ifnum \c@secnumdepth>\m@ne + \@chapapp\ \thechapter. \ \fi ##1}}{}}% +\def\sectionmark##1{\markright{\MakeUppercase{\ifnum \c@secnumdepth >\z@ + \thesection. \ \fi ##1}}}}% +%\csname ps@headings\endcsname % use \ps@headings defaults if they exist +\ps@@fancy +\gdef\ps@fancy{\@fancyplainfalse\ps@@fancy}% +% Initialize \headwidth if the user didn't +% +\ifdim\headwidth<0sp +% +% This catches the case that \headwidth hasn't been initialized and the +% case that the user added something to \headwidth in the expectation that +% it was initialized to \textwidth. We compensate this now. This loses if +% the user intended to multiply it by a factor. But that case is more +% likely done by saying something like \headwidth=1.2\textwidth. +% The doc says you have to change \headwidth after the first call to +% \pagestyle{fancy}. This code is just to catch the most common cases were +% that requirement is violated. +% + \global\advance\headwidth123456789sp\global\advance\headwidth\textwidth +\fi} +\def\ps@fancyplain{\ps@fancy \let\ps@plain\ps@plain@fancy} +\def\ps@plain@fancy{\@fancyplaintrue\ps@@fancy} +\let\ps@@empty\ps@empty +\def\ps@@fancy{% +\ps@@empty % This is for amsbook/amsart, which do strange things with \topskip +\def\@mkboth{\protect\markboth}% +\def\@oddhead{\@fancyhead\fancy@Oolh\f@ncyolh\f@ncyoch\f@ncyorh\fancy@Oorh}% +\def\@oddfoot{\@fancyfoot\fancy@Oolf\f@ncyolf\f@ncyocf\f@ncyorf\fancy@Oorf}% +\def\@evenhead{\@fancyhead\fancy@Oelh\f@ncyelh\f@ncyech\f@ncyerh\fancy@Oerh}% +\def\@evenfoot{\@fancyfoot\fancy@Oelf\f@ncyelf\f@ncyecf\f@ncyerf\fancy@Oerf}% +} +% Default definitions for compatibility mode: +% These cause the header/footer to take the defined \headwidth as width +% And to shift in the direction of the marginpar area + +\def\fancy@Oolh{\if@reversemargin\hss\else\relax\fi} +\def\fancy@Oorh{\if@reversemargin\relax\else\hss\fi} +\let\fancy@Oelh\fancy@Oorh +\let\fancy@Oerh\fancy@Oolh + +\let\fancy@Oolf\fancy@Oolh +\let\fancy@Oorf\fancy@Oorh +\let\fancy@Oelf\fancy@Oelh +\let\fancy@Oerf\fancy@Oerh + +% New definitions for the use of \fancyhfoffset +% These calculate the \headwidth from \textwidth and the specified offsets. + +\def\fancy@offsolh{\headwidth=\textwidth\advance\headwidth\f@ncyO@olh + \advance\headwidth\f@ncyO@orh\hskip-\f@ncyO@olh} +\def\fancy@offselh{\headwidth=\textwidth\advance\headwidth\f@ncyO@elh + \advance\headwidth\f@ncyO@erh\hskip-\f@ncyO@elh} + +\def\fancy@offsolf{\headwidth=\textwidth\advance\headwidth\f@ncyO@olf + \advance\headwidth\f@ncyO@orf\hskip-\f@ncyO@olf} +\def\fancy@offself{\headwidth=\textwidth\advance\headwidth\f@ncyO@elf + \advance\headwidth\f@ncyO@erf\hskip-\f@ncyO@elf} + +\def\fancy@setoffs{% +% Just in case \let\headwidth\textwidth was used + \fancy@gbl\let\headwidth\fancy@headwidth + \fancy@gbl\let\fancy@Oolh\fancy@offsolh + \fancy@gbl\let\fancy@Oelh\fancy@offselh + \fancy@gbl\let\fancy@Oorh\hss + \fancy@gbl\let\fancy@Oerh\hss + \fancy@gbl\let\fancy@Oolf\fancy@offsolf + \fancy@gbl\let\fancy@Oelf\fancy@offself + \fancy@gbl\let\fancy@Oorf\hss + \fancy@gbl\let\fancy@Oerf\hss} + +\newif\iffootnote +\let\latex@makecol\@makecol +\def\@makecol{\ifvoid\footins\footnotetrue\else\footnotefalse\fi +\let\topfloat\@toplist\let\botfloat\@botlist\latex@makecol} +\def\iftopfloat#1#2{\ifx\topfloat\empty #2\else #1\fi} +\def\ifbotfloat#1#2{\ifx\botfloat\empty #2\else #1\fi} +\def\iffloatpage#1#2{\if@fcolmade #1\else #2\fi} + +\newcommand{\fancypagestyle}[2]{% + \@namedef{ps@#1}{\let\fancy@gbl\relax#2\relax\ps@fancy}} diff --git a/docs/ICML_workshop/icml2023/icml2023.bst b/docs/ICML_workshop/icml2023/icml2023.bst new file mode 100644 index 0000000..070cf4a --- /dev/null +++ b/docs/ICML_workshop/icml2023/icml2023.bst @@ -0,0 +1,1443 @@ +%% File: `icml2023.bst' +%% A modification of `plainnl.bst' for use with natbib package +%% +%% Copyright 2010 Hal Daum\'e III +%% Modified by J. Fürnkranz +%% - Changed labels from (X and Y, 2000) to (X & Y, 2000) +%% - Changed References to last name first and abbreviated first names. +%% Modified by Iain Murray 2018 (who suggests adopting a standard .bst in future...) +%% - Made it actually use abbreviated first names +%% +%% Copyright 1993-2007 Patrick W Daly +%% Max-Planck-Institut f\"ur Sonnensystemforschung +%% Max-Planck-Str. 2 +%% D-37191 Katlenburg-Lindau +%% Germany +%% E-mail: daly@mps.mpg.de +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN +%% archives in directory macros/latex/base/lppl.txt; either +%% version 1 of the License, or any later version. +%% + % Version and source file information: + % \ProvidesFile{icml2010.mbs}[2007/11/26 1.93 (PWD)] + % + % BibTeX `plainnat' family + % version 0.99b for BibTeX versions 0.99a or later, + % for LaTeX versions 2.09 and 2e. + % + % For use with the `natbib.sty' package; emulates the corresponding + % member of the `plain' family, but with author-year citations. + % + % With version 6.0 of `natbib.sty', it may also be used for numerical + % citations, while retaining the commands \citeauthor, \citefullauthor, + % and \citeyear to print the corresponding information. + % + % For version 7.0 of `natbib.sty', the KEY field replaces missing + % authors/editors, and the date is left blank in \bibitem. + % + % Includes field EID for the sequence/citation number of electronic journals + % which is used instead of page numbers. + % + % Includes fields ISBN and ISSN. + % + % Includes field URL for Internet addresses. + % + % Includes field DOI for Digital Object Idenfifiers. + % + % Works best with the url.sty package of Donald Arseneau. + % + % Works with identical authors and year are further sorted by + % citation key, to preserve any natural sequence. + % +ENTRY + { address + author + booktitle + chapter + doi + eid + edition + editor + howpublished + institution + isbn + issn + journal + key + month + note + number + organization + pages + publisher + school + series + title + type + url + volume + year + } + {} + { label extra.label sort.label short.list } + +INTEGERS { output.state before.all mid.sentence after.sentence after.block } + +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} + +STRINGS { s t } + +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} + +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} + +FUNCTION {new.block.checka} +{ empty$ + 'skip$ + 'new.block + if$ +} + +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} + +FUNCTION {new.sentence.checka} +{ empty$ + 'skip$ + 'new.sentence + if$ +} + +FUNCTION {new.sentence.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.sentence + if$ +} + +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} + +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "\emph{" swap$ * "}" * } + if$ +} + +INTEGERS { nameptr namesleft numnames } + +FUNCTION {format.names} +{ 's := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr "{vv~}{ll}{, jj}{, f.}" format.name$ 't := + nameptr #1 > + { namesleft #1 > + { ", " * t * } + { numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {format.key} +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.authors} +{ author empty$ + { "" } + { author format.names } + if$ +} + +FUNCTION {format.editors} +{ editor empty$ + { "" } + { editor format.names + editor num.names$ #1 > + { " (eds.)" * } + { " (ed.)" * } + if$ + } + if$ +} + +FUNCTION {format.isbn} +{ isbn empty$ + { "" } + { new.block "ISBN " isbn * } + if$ +} + +FUNCTION {format.issn} +{ issn empty$ + { "" } + { new.block "ISSN " issn * } + if$ +} + +FUNCTION {format.url} +{ url empty$ + { "" } + { new.block "URL \url{" url * "}" * } + if$ +} + +FUNCTION {format.doi} +{ doi empty$ + { "" } + { new.block "\doi{" doi * "}" * } + if$ +} + +FUNCTION {format.title} +{ title empty$ + { "" } + { title "t" change.case$ } + if$ +} + +FUNCTION {format.full.names} +{'s := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}" format.name$ 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {author.editor.full} +{ author empty$ + { editor empty$ + { "" } + { editor format.full.names } + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {author.full} +{ author empty$ + { "" } + { author format.full.names } + if$ +} + +FUNCTION {editor.full} +{ editor empty$ + { "" } + { editor format.full.names } + if$ +} + +FUNCTION {make.full.names} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.full + { type$ "proceedings" = + 'editor.full + 'author.full + if$ + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[" write$ + label write$ + ")" make.full.names duplicate$ short.list = + { pop$ } + { * } + if$ + "]{" * write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {n.dashify} +{ 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {format.date} +{ year duplicate$ empty$ + { "empty year in " cite$ * warning$ + pop$ "" } + 'skip$ + if$ + month empty$ + 'skip$ + { month + " " * swap$ * + } + if$ + extra.label * +} + +FUNCTION {format.btitle} +{ title emphasize +} + +FUNCTION {tie.or.space.connect} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ * * +} + +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { "volume" volume tie.or.space.connect + series empty$ + 'skip$ + { " of " * series emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} + +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { output.state mid.sentence = + { "number" } + { "Number" } + if$ + number tie.or.space.connect + series empty$ + { "there's a number but no series in " cite$ * warning$ } + { " in " * series * } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {format.edition} +{ edition empty$ + { "" } + { output.state mid.sentence = + { edition "l" change.case$ " edition" * } + { edition "t" change.case$ " edition" * } + if$ + } + if$ +} + +INTEGERS { multiresult } + +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {format.pages} +{ pages empty$ + { "" } + { pages multi.page.check + { "pp.\ " pages n.dashify tie.or.space.connect } + { "pp.\ " pages tie.or.space.connect } + if$ + } + if$ +} + +FUNCTION {format.eid} +{ eid empty$ + { "" } + { "art." eid tie.or.space.connect } + if$ +} + +FUNCTION {format.vol.num.pages} +{ volume field.or.null + number empty$ + 'skip$ + { "\penalty0 (" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + pages empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.pages } + { ":\penalty0 " * pages n.dashify * } + if$ + } + if$ +} + +FUNCTION {format.vol.num.eid} +{ volume field.or.null + number empty$ + 'skip$ + { "\penalty0 (" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + eid empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.eid } + { ":\penalty0 " * eid * } + if$ + } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + 'format.pages + { type empty$ + { "chapter" } + { type "l" change.case$ } + if$ + chapter tie.or.space.connect + pages empty$ + 'skip$ + { ", " * format.pages * } + if$ + } + if$ +} + +FUNCTION {format.in.ed.booktitle} +{ booktitle empty$ + { "" } + { editor empty$ + { "In " booktitle emphasize * } + { "In " format.editors * ", " * booktitle emphasize * } + if$ + } + if$ +} + +FUNCTION {empty.misc.check} +{ author empty$ title empty$ howpublished empty$ + month empty$ year empty$ note empty$ + and and and and and + key empty$ not and + { "all relevant fields are empty in " cite$ * warning$ } + 'skip$ + if$ +} + +FUNCTION {format.thesis.type} +{ type empty$ + 'skip$ + { pop$ + type "t" change.case$ + } + if$ +} + +FUNCTION {format.tr.number} +{ type empty$ + { "Technical Report" } + 'type + if$ + number empty$ + { "t" change.case$ } + { number tie.or.space.connect } + if$ +} + +FUNCTION {format.article.crossref} +{ key empty$ + { journal empty$ + { "need key or journal for " cite$ * " to crossref " * crossref * + warning$ + "" + } + { "In \emph{" journal * "}" * } + if$ + } + { "In " } + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {format.book.crossref} +{ volume empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + "In " + } + { "Volume" volume tie.or.space.connect + " of " * + } + if$ + editor empty$ + editor field.or.null author field.or.null = + or + { key empty$ + { series empty$ + { "need editor, key, or series for " cite$ * " to crossref " * + crossref * warning$ + "" * + } + { "\emph{" * series * "}" * } + if$ + } + 'skip$ + if$ + } + 'skip$ + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {format.incoll.inproc.crossref} +{ editor empty$ + editor field.or.null author field.or.null = + or + { key empty$ + { booktitle empty$ + { "need editor, key, or booktitle for " cite$ * " to crossref " * + crossref * warning$ + "" + } + { "In \emph{" booktitle * "}" * } + if$ + } + { "In " } + if$ + } + { "In " } + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {article} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { journal emphasize "journal" output.check + eid empty$ + { format.vol.num.pages output } + { format.vol.num.eid output } + if$ + format.date "year" output.check + } + { format.article.crossref output.nonnull + eid empty$ + { format.pages output } + { format.eid output } + if$ + } + if$ + format.issn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {book} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.date "year" output.check + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {booklet} +{ output.bibitem + format.authors output + author format.key output + new.block + format.title "title" output.check + howpublished address new.block.checkb + howpublished output + address output + format.date output + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {inbook} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + format.chapter.pages "chapter and pages" output.check + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { format.chapter.pages "chapter and pages" output.check + new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.date "year" output.check + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {incollection} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.chapter.pages output + new.sentence + publisher "publisher" output.check + address output + format.edition output + format.date "year" output.check + } + { format.incoll.inproc.crossref output.nonnull + format.chapter.pages output + } + if$ + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {inproceedings} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.pages output + address empty$ + { organization publisher new.sentence.checkb + organization output + publisher output + format.date "year" output.check + } + { address output.nonnull + format.date "year" output.check + new.sentence + organization output + publisher output + } + if$ + } + { format.incoll.inproc.crossref output.nonnull + format.pages output + } + if$ + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {conference} { inproceedings } + +FUNCTION {manual} +{ output.bibitem + format.authors output + author format.key output + new.block + format.btitle "title" output.check + organization address new.block.checkb + organization output + address output + format.edition output + format.date output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {mastersthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + "Master's thesis" format.thesis.type output.nonnull + school "school" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {misc} +{ output.bibitem + format.authors output + author format.key output + title howpublished new.block.checkb + format.title output + howpublished new.block.checka + howpublished output + format.date output + format.issn output + format.url output + new.block + note output + fin.entry + empty.misc.check +} + +FUNCTION {phdthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.btitle "title" output.check + new.block + "PhD thesis" format.thesis.type output.nonnull + school "school" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {proceedings} +{ output.bibitem + format.editors output + editor format.key output + new.block + format.btitle "title" output.check + format.bvolume output + format.number.series output + address output + format.date "year" output.check + new.sentence + organization output + publisher output + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {techreport} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + format.tr.number output.nonnull + institution "institution" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {unpublished} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + note "note" output.check + format.date output + format.url output + fin.entry +} + +FUNCTION {default.type} { misc } + + +MACRO {jan} {"January"} + +MACRO {feb} {"February"} + +MACRO {mar} {"March"} + +MACRO {apr} {"April"} + +MACRO {may} {"May"} + +MACRO {jun} {"June"} + +MACRO {jul} {"July"} + +MACRO {aug} {"August"} + +MACRO {sep} {"September"} + +MACRO {oct} {"October"} + +MACRO {nov} {"November"} + +MACRO {dec} {"December"} + + + +MACRO {acmcs} {"ACM Computing Surveys"} + +MACRO {acta} {"Acta Informatica"} + +MACRO {cacm} {"Communications of the ACM"} + +MACRO {ibmjrd} {"IBM Journal of Research and Development"} + +MACRO {ibmsj} {"IBM Systems Journal"} + +MACRO {ieeese} {"IEEE Transactions on Software Engineering"} + +MACRO {ieeetc} {"IEEE Transactions on Computers"} + +MACRO {ieeetcad} + {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"} + +MACRO {ipl} {"Information Processing Letters"} + +MACRO {jacm} {"Journal of the ACM"} + +MACRO {jcss} {"Journal of Computer and System Sciences"} + +MACRO {scp} {"Science of Computer Programming"} + +MACRO {sicomp} {"SIAM Journal on Computing"} + +MACRO {tocs} {"ACM Transactions on Computer Systems"} + +MACRO {tods} {"ACM Transactions on Database Systems"} + +MACRO {tog} {"ACM Transactions on Graphics"} + +MACRO {toms} {"ACM Transactions on Mathematical Software"} + +MACRO {toois} {"ACM Transactions on Office Information Systems"} + +MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"} + +MACRO {tcs} {"Theoretical Computer Science"} + + +READ + +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} + +INTEGERS { len } + +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} + +FUNCTION {format.lab.names} +{ 's := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ " et~al." * } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { " et~al." * } + { " \& " * s #2 "{vv~}{ll}" format.name$ * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.key.organization.label} +{ author empty$ + { key empty$ + { organization empty$ + { cite$ #1 #3 substring$ } + { "The " #4 organization chop.word #3 text.prefix$ } + if$ + } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.organization.label} +{ editor empty$ + { key empty$ + { organization empty$ + { cite$ #1 #3 substring$ } + { "The " #4 organization chop.word #3 text.prefix$ } + if$ + } + 'key + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.short.authors} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.organization.label + { type$ "manual" = + 'author.key.organization.label + 'author.key.label + if$ + } + if$ + } + if$ + 'short.list := +} + +FUNCTION {calc.label} +{ calc.short.authors + short.list + "(" + * + year duplicate$ empty$ + short.list key field.or.null = or + { pop$ "" } + 'skip$ + if$ + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { + s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't := + nameptr #1 > + { + " " * + namesleft #1 = t "others" = and + { "zzzzz" * } + { numnames #2 > nameptr #2 = and + { "zz" * year field.or.null * " " * } + 'skip$ + if$ + t sortify * + } + if$ + } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} + +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.organization.sort} +{ author empty$ + { organization empty$ + { key empty$ + { "to sort, need author, organization, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { "The " #4 organization chop.word sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {editor.organization.sort} +{ editor empty$ + { organization empty$ + { key empty$ + { "to sort, need editor, organization, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { "The " #4 organization chop.word sortify } + if$ + } + { editor sort.format.names } + if$ +} + + +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.organization.sort + { type$ "manual" = + 'author.organization.sort + 'author.sort + if$ + } + if$ + } + if$ + " " + * + year field.or.null sortify + * + " " + * + cite$ + * + #1 entry.max$ substring$ + 'sort.label := + sort.label * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} + +SORT + +STRINGS { longest.label last.label next.extra } + +INTEGERS { longest.label.width last.extra.num number.label } + +FUNCTION {initialize.longest.label} +{ "" 'longest.label := + #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'longest.label.width := + #0 'last.extra.num := + #0 'number.label := +} + +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ + number.label #1 + 'number.label := +} + +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + extra.label 'next.extra := + extra.label + duplicate$ empty$ + 'skip$ + { "{\natexlab{" swap$ * "}}" * } + if$ + 'extra.label := + label extra.label * 'label := +} + +EXECUTE {initialize.longest.label} + +ITERATE {forward.pass} + +REVERSE {reverse.pass} + +FUNCTION {bib.sort.order} +{ sort.label 'sort.key$ := +} + +ITERATE {bib.sort.order} + +SORT + +FUNCTION {begin.bib} +{ preamble$ empty$ + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" number.label int.to.str$ * "}" * + write$ newline$ + "\providecommand{\natexlab}[1]{#1}" + write$ newline$ + "\providecommand{\url}[1]{\texttt{#1}}" + write$ newline$ + "\expandafter\ifx\csname urlstyle\endcsname\relax" + write$ newline$ + " \providecommand{\doi}[1]{doi: #1}\else" + write$ newline$ + " \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi" + write$ newline$ +} + +EXECUTE {begin.bib} + +EXECUTE {init.state.consts} + +ITERATE {call.type$} + +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} + +EXECUTE {end.bib} diff --git a/docs/ICML_workshop/icml2023/icml2023.sty b/docs/ICML_workshop/icml2023/icml2023.sty new file mode 100644 index 0000000..10f902d --- /dev/null +++ b/docs/ICML_workshop/icml2023/icml2023.sty @@ -0,0 +1,803 @@ +% File: icml2023.sty (LaTeX style file for ICML-2023, version of 2023-04-25) + +% This file contains the LaTeX formatting parameters for a two-column +% conference proceedings that is 8.5 inches wide by 11 inches high. +% +% Modified by Sivan Sabato 2023: changed years and volume number. +% Modified by Jonathan Scarlett 2023: added page numbers to every page +% +% Modified by Csaba Szepesvari 2022: changed years, PMLR ref. Turned off checking marginparwidth +% as marginparwidth only controls the space available for margin notes and margin notes +% will NEVER be used anyways in submitted versions, so there is no reason one should +% check whether marginparwidth has been tampered with. +% Also removed pdfview=FitH from hypersetup as it did not do its job; the default choice is a bit better +% but of course the double-column format is not supported by this hyperlink preview functionality +% in a completely satisfactory fashion. +% Modified by Gang Niu 2022: Changed color to xcolor +% +% Modified by Iain Murray 2018: changed years, location. Remove affiliation notes when anonymous. +% Move times dependency from .tex to .sty so fewer people delete it. +% +% Modified by Daniel Roy 2017: changed byline to use footnotes for affiliations, and removed emails +% +% Modified by Percy Liang 12/2/2013: changed the year, location from the previous template for ICML 2014 + +% Modified by Fei Sha 9/2/2013: changed the year, location form the previous template for ICML 2013 +% +% Modified by Fei Sha 4/24/2013: (1) remove the extra whitespace after the first author's email address (in %the camera-ready version) (2) change the Proceeding ... of ICML 2010 to 2014 so PDF's metadata will show up % correctly +% +% Modified by Sanjoy Dasgupta, 2013: changed years, location +% +% Modified by Francesco Figari, 2012: changed years, location +% +% Modified by Christoph Sawade and Tobias Scheffer, 2011: added line +% numbers, changed years +% +% Modified by Hal Daume III, 2010: changed years, added hyperlinks +% +% Modified by Kiri Wagstaff, 2009: changed years +% +% Modified by Sam Roweis, 2008: changed years +% +% Modified by Ricardo Silva, 2007: update of the ifpdf verification +% +% Modified by Prasad Tadepalli and Andrew Moore, merely changing years. +% +% Modified by Kristian Kersting, 2005, based on Jennifer Dy's 2004 version +% - running title. If the original title is to long or is breaking a line, +% use \icmltitlerunning{...} in the preamble to supply a shorter form. +% Added fancyhdr package to get a running head. +% - Updated to store the page size because pdflatex does compile the +% page size into the pdf. +% +% Hacked by Terran Lane, 2003: +% - Updated to use LaTeX2e style file conventions (ProvidesPackage, +% etc.) +% - Added an ``appearing in'' block at the base of the first column +% (thus keeping the ``appearing in'' note out of the bottom margin +% where the printer should strip in the page numbers). +% - Added a package option [accepted] that selects between the ``Under +% review'' notice (default, when no option is specified) and the +% ``Appearing in'' notice (for use when the paper has been accepted +% and will appear). +% +% Originally created as: ml2k.sty (LaTeX style file for ICML-2000) +% by P. Langley (12/23/99) + +%%%%%%%%%%%%%%%%%%%% +%% This version of the style file supports both a ``review'' version +%% and a ``final/accepted'' version. The difference is only in the +%% text that appears in the note at the bottom of the first column of +%% the first page. The default behavior is to print a note to the +%% effect that the paper is under review and don't distribute it. The +%% final/accepted version prints an ``Appearing in'' note. To get the +%% latter behavior, in the calling file change the ``usepackage'' line +%% from: +%% \usepackage{icml2023} +%% to +%% \usepackage[accepted]{icml2023} +%%%%%%%%%%%%%%%%%%%% + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{icml2023}[2023/01/03 v2.0 ICML Conference Style File] + +% Before 2018, \usepackage{times} was in the example TeX, but inevitably +% not everybody did it. +\RequirePackage{times} + +% Use fancyhdr package +\RequirePackage{fancyhdr} +\RequirePackage{xcolor} % changed from color to xcolor (2021/11/24) +\RequirePackage{algorithm} +\RequirePackage{algorithmic} +\RequirePackage{natbib} +\RequirePackage{eso-pic} % used by \AddToShipoutPicture +\RequirePackage{forloop} +\RequirePackage{url} + +%%%%%%%% Options +\DeclareOption{accepted}{% + \renewcommand{\Notice@String}{\ICML@appearing} + \gdef\isaccepted{1} +} + +\DeclareOption{nohyperref}{% + \gdef\nohyperref{1} +} + + + +%%%%%%%%%%%%%%%%%%%% +% This string is printed at the bottom of the page for the +% final/accepted version of the ``appearing in'' note. Modify it to +% change that text. +%%%%%%%%%%%%%%%%%%%% +\newcommand{\ICML@appearing}{\textit{Proceedings of the +$\mathit{40}^{th}$ International Conference on Machine Learning}, +Honolulu, Hawaii, USA. PMLR 202, 2023. +Copyright 2023 by the author(s).} + +%%%%%%%%%%%%%%%%%%%% +% This string is printed at the bottom of the page for the draft/under +% review version of the ``appearing in'' note. Modify it to change +% that text. +%%%%%%%%%%%%%%%%%%%% +\newcommand{\Notice@String}{Preliminary work. Under review by the +International Conference on Machine Learning (ICML)\@. Do not distribute.} + +% Cause the declared options to actually be parsed and activated +\ProcessOptions\relax + +\ifdefined\isaccepted\else\ifdefined\hypersetup + \hypersetup{pdfauthor={Anonymous Authors}} + \fi +\fi + +\ifdefined\nohyperref\else\ifdefined\hypersetup + \definecolor{mydarkblue}{rgb}{0,0.08,0.45} + \hypersetup{ % + pdftitle={}, + pdfsubject={Proceedings of the International Conference on Machine Learning 2023}, + pdfkeywords={}, + pdfborder=0 0 0, + pdfpagemode=UseNone, + colorlinks=true, + linkcolor=mydarkblue, + citecolor=mydarkblue, + filecolor=mydarkblue, + urlcolor=mydarkblue, + } + + + \fi +\fi + + + +% Uncomment the following for debugging. It will cause LaTeX to dump +% the version of the ``appearing in'' string that will actually appear +% in the document. +%\typeout{>> Notice string='\Notice@String'} + +% Change citation commands to be more like old ICML styles +\newcommand{\yrcite}[1]{\citeyearpar{#1}} +\renewcommand{\cite}[1]{\citep{#1}} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% to ensure the letter format is used. pdflatex does compile the +% page size into the pdf. This is done using \pdfpagewidth and +% \pdfpageheight. As Latex does not know this directives, we first +% check whether pdflatex or latex is used. +% +% Kristian Kersting 2005 +% +% in order to account for the more recent use of pdfetex as the default +% compiler, I have changed the pdf verification. +% +% Ricardo Silva 2007 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\paperwidth=8.5in +\paperheight=11in + +% old PDFLaTex verification, circa 2005 +% +%\newif\ifpdf\ifx\pdfoutput\undefined +% \pdffalse % we are not running PDFLaTeX +%\else +% \pdfoutput=1 % we are running PDFLaTeX +% \pdftrue +%\fi + +\newif\ifpdf %adapted from ifpdf.sty +\ifx\pdfoutput\undefined +\else + \ifx\pdfoutput\relax + \else + \ifcase\pdfoutput + \else + \pdftrue + \fi + \fi +\fi + +\ifpdf +% \pdfpagewidth=\paperwidth +% \pdfpageheight=\paperheight + \setlength{\pdfpagewidth}{8.5in} + \setlength{\pdfpageheight}{11in} +\fi + +% Physical page layout + +\evensidemargin -0.23in +\oddsidemargin -0.23in +\setlength\textheight{9.0in} +\setlength\textwidth{6.75in} +\setlength\columnsep{0.25in} +\setlength\headheight{10pt} +\setlength\headsep{10pt} +\addtolength{\topmargin}{-20pt} +\addtolength{\topmargin}{-0.29in} + +% Historically many authors tried to include packages like geometry or fullpage, +% which change the page layout. It either makes the proceedings inconsistent, or +% wastes organizers' time chasing authors. So let's nip these problems in the +% bud here. -- Iain Murray 2018. +%\RequirePackage{printlen} +\AtBeginDocument{% +% To get the numbers below, include printlen package above and see lengths like this: +%\printlength\oddsidemargin\\ +%\printlength\headheight\\ +%\printlength\textheight\\ +%\printlength\marginparsep\\ +%\printlength\footskip\\ +%\printlength\hoffset\\ +%\printlength\paperwidth\\ +%\printlength\topmargin\\ +%\printlength\headsep\\ +%\printlength\textwidth\\ +%\printlength\marginparwidth\\ +%\printlength\marginparpush\\ +%\printlength\voffset\\ +%\printlength\paperheight\\ +% +\newif\ifmarginsmessedwith +\marginsmessedwithfalse +\ifdim\oddsidemargin=-16.62178pt \else oddsidemargin has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\headheight=10.0pt \else headheight has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\textheight=650.43pt \else textheight has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\marginparsep=11.0pt \else marginparsep has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\footskip=25.0pt \else footskip has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\hoffset=0.0pt \else hoffset has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\paperwidth=614.295pt \else paperwidth has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\topmargin=-24.95781pt \else topmargin has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\headsep=10.0pt \else headsep has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\textwidth=487.8225pt \else textwidth has been altered.\\ \marginsmessedwithtrue\fi +%\ifdim\marginparwidth=65.0pt \else marginparwidth has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\marginparpush=5.0pt \else marginparpush has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\voffset=0.0pt \else voffset has been altered.\\ \marginsmessedwithtrue\fi +\ifdim\paperheight=794.96999pt \else paperheight has been altered.\\ \marginsmessedwithtrue\fi +\ifmarginsmessedwith + +\textbf{\large \em The page layout violates the ICML style.} + +Please do not change the page layout, or include packages like geometry, +savetrees, or fullpage, which change it for you. + +We're not able to reliably undo arbitrary changes to the style. Please remove +the offending package(s), or layout-changing commands and try again. + +\fi} + + +%% The following is adapted from code in the acmconf.sty conference +%% style file. The constants in it are somewhat magical, and appear +%% to work well with the two-column format on US letter paper that +%% ICML uses, but will break if you change that layout, or if you use +%% a longer block of text for the copyright notice string. Fiddle with +%% them if necessary to get the block to fit/look right. +%% +%% -- Terran Lane, 2003 +%% +%% The following comments are included verbatim from acmconf.sty: +%% +%%% This section (written by KBT) handles the 1" box in the lower left +%%% corner of the left column of the first page by creating a picture, +%%% and inserting the predefined string at the bottom (with a negative +%%% displacement to offset the space allocated for a non-existent +%%% caption). +%%% +\def\ftype@copyrightbox{8} +\def\@copyrightspace{ +% Create a float object positioned at the bottom of the column. Note +% that because of the mystical nature of floats, this has to be called +% before the first column is populated with text (e.g., from the title +% or abstract blocks). Otherwise, the text will force the float to +% the next column. -- TDRL. +\@float{copyrightbox}[b] +\begin{center} +\setlength{\unitlength}{1pc} +\begin{picture}(20,1.5) +% Create a line separating the main text from the note block. +% 4.818pc==0.8in. +\put(0,2.5){\line(1,0){4.818}} +% Insert the text string itself. Note that the string has to be +% enclosed in a parbox -- the \put call needs a box object to +% position. Without the parbox, the text gets splattered across the +% bottom of the page semi-randomly. The 19.75pc distance seems to be +% the width of the column, though I can't find an appropriate distance +% variable to substitute here. -- TDRL. +\put(0,0){\parbox[b]{19.75pc}{\small \Notice@String}} +\end{picture} +\end{center} +\end@float} + +% Note: A few Latex versions need the next line instead of the former. +% \addtolength{\topmargin}{0.3in} +% \setlength\footheight{0pt} +\setlength\footskip{25.0pt} +%\pagestyle{empty} +\flushbottom \twocolumn +\sloppy + +% Clear out the addcontentsline command +\def\addcontentsline#1#2#3{} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% commands for formatting paper title, author names, and addresses. + +%%start%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%% title as running head -- Kristian Kersting 2005 %%%%%%%%%%%%% + + +%\makeatletter +%\newtoks\mytoksa +%\newtoks\mytoksb +%\newcommand\addtomylist[2]{% +% \mytoksa\expandafter{#1}% +% \mytoksb{#2}% +% \edef#1{\the\mytoksa\the\mytoksb}% +%} +%\makeatother + +% box to check the size of the running head +\newbox\titrun + +% general page style +\pagestyle{fancy} +\fancyhf{} +\fancyhead{} +\fancyfoot{} +\cfoot{\thepage} +% set the width of the head rule to 1 point +\renewcommand{\headrulewidth}{1pt} + +% definition to set the head as running head in the preamble +\def\icmltitlerunning#1{\gdef\@icmltitlerunning{#1}} + +% main definition adapting \icmltitle from 2004 +\long\def\icmltitle#1{% + + %check whether @icmltitlerunning exists + % if not \icmltitle is used as running head + \ifx\undefined\@icmltitlerunning% + \gdef\@icmltitlerunning{#1} + \fi + + %add it to pdf information + \ifdefined\nohyperref\else\ifdefined\hypersetup + \hypersetup{pdftitle={#1}} + \fi\fi + + %get the dimension of the running title + \global\setbox\titrun=\vbox{\small\bf\@icmltitlerunning} + + % error flag + \gdef\@runningtitleerror{0} + + % running title too long + \ifdim\wd\titrun>\textwidth% + {\gdef\@runningtitleerror{1}}% + % running title breaks a line + \else\ifdim\ht\titrun>6.25pt + {\gdef\@runningtitleerror{2}}% + \fi + \fi + + % if there is somthing wrong with the running title + \ifnum\@runningtitleerror>0 + \typeout{}% + \typeout{}% + \typeout{*******************************************************}% + \typeout{Title exceeds size limitations for running head.}% + \typeout{Please supply a shorter form for the running head} + \typeout{with \string\icmltitlerunning{...}\space prior to \string\begin{document}}% + \typeout{*******************************************************}% + \typeout{}% + \typeout{}% + % set default running title + \chead{\small\bf Title Suppressed Due to Excessive Size}% + \else + % 'everything' fine, set provided running title + \chead{\small\bf\@icmltitlerunning}% + \fi + + % no running title on the first page of the paper + \thispagestyle{plain} + +%%%%%%%%%%%%%%%%%%%% Kristian Kersting %%%%%%%%%%%%%%%%%%%%%%%%% +%end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + {\center\baselineskip 18pt + \toptitlebar{\Large\bf #1}\bottomtitlebar} +} + + +\gdef\icmlfullauthorlist{} +\newcommand\addstringtofullauthorlist{\g@addto@macro\icmlfullauthorlist} +\newcommand\addtofullauthorlist[1]{% + \ifdefined\icmlanyauthors% + \addstringtofullauthorlist{, #1}% + \else% + \addstringtofullauthorlist{#1}% + \gdef\icmlanyauthors{1}% + \fi% +% \ifdefined\nohyperref\else + \ifdefined\hypersetup% + \hypersetup{pdfauthor=\icmlfullauthorlist}% + \fi%\fi + } + + +\def\toptitlebar{\hrule height1pt \vskip .25in} +\def\bottomtitlebar{\vskip .22in \hrule height1pt \vskip .3in} + +\newenvironment{icmlauthorlist}{% + \setlength\topsep{0pt} + \setlength\parskip{0pt} + \begin{center} +}{% + \end{center} +} + +\newcounter{@affiliationcounter} +\newcommand{\@pa}[1]{% +% ``#1'' +\ifcsname the@affil#1\endcsname + % do nothing +\else + \ifcsname @icmlsymbol#1\endcsname + % nothing + \else + \stepcounter{@affiliationcounter}% + \newcounter{@affil#1}% + \setcounter{@affil#1}{\value{@affiliationcounter}}% + \fi +\fi% +\ifcsname @icmlsymbol#1\endcsname + \textsuperscript{\csname @icmlsymbol#1\endcsname\,}% +\else + %\expandafter\footnotemark[\arabic{@affil#1}\,]% + \textsuperscript{\arabic{@affil#1}\,}% +\fi +} + +%\newcommand{\icmlauthor}[2]{% +%\addtofullauthorlist{#1}% +%#1\@for\theaffil:=#2\do{\pa{\theaffil}}% +%} +\newcommand{\icmlauthor}[2]{% + \ifdefined\isaccepted + \mbox{\bf #1}\,\@for\theaffil:=#2\do{\@pa{\theaffil}} \addtofullauthorlist{#1}% + \else + \ifdefined\@icmlfirsttime + \else + \gdef\@icmlfirsttime{1} + \mbox{\bf Anonymous Authors}\@pa{@anon} \addtofullauthorlist{Anonymous Authors} + \fi + \fi +} + + + + +\newcommand{\icmlsetsymbol}[2]{% + \expandafter\gdef\csname @icmlsymbol#1\endcsname{#2} + } + + +\newcommand{\icmlaffiliation}[2]{% +\ifdefined\isaccepted +\ifcsname the@affil#1\endcsname + \expandafter\gdef\csname @affilname\csname the@affil#1\endcsname\endcsname{#2}% +\else + {\bf AUTHORERR: Error in use of \textbackslash{}icmlaffiliation command. Label ``#1'' not mentioned in some \textbackslash{}icmlauthor\{author name\}\{labels here\} command beforehand. } + \typeout{}% + \typeout{}% + \typeout{*******************************************************}% + \typeout{Affiliation label undefined. }% + \typeout{Make sure \string\icmlaffiliation\space follows } + \typeout{all of \string\icmlauthor\space commands}% + \typeout{*******************************************************}% + \typeout{}% + \typeout{}% +\fi +\else % \isaccepted + % can be called multiple times... it's idempotent + \expandafter\gdef\csname @affilname1\endcsname{Anonymous Institution, Anonymous City, Anonymous Region, Anonymous Country} +\fi +} + +\newcommand{\icmlcorrespondingauthor}[2]{ +\ifdefined\isaccepted + \ifdefined\icmlcorrespondingauthor@text + \g@addto@macro\icmlcorrespondingauthor@text{, #1 \textless{}#2\textgreater{}} + \else + \gdef\icmlcorrespondingauthor@text{#1 \textless{}#2\textgreater{}} + \fi +\else +\gdef\icmlcorrespondingauthor@text{Anonymous Author \textless{}anon.email@domain.com\textgreater{}} +\fi +} + +\newcommand{\icmlEqualContribution}{\textsuperscript{*}Equal contribution } + +\newcounter{@affilnum} +\newcommand{\printAffiliationsAndNotice}[1]{% +\stepcounter{@affiliationcounter}% +{\let\thefootnote\relax\footnotetext{\hspace*{-\footnotesep}\ifdefined\isaccepted #1\fi% +\forloop{@affilnum}{1}{\value{@affilnum} < \value{@affiliationcounter}}{ +\textsuperscript{\arabic{@affilnum}}\ifcsname @affilname\the@affilnum\endcsname% +\csname @affilname\the@affilnum\endcsname% +\else +{\bf AUTHORERR: Missing \textbackslash{}icmlaffiliation.} +\fi +}. +\ifdefined\icmlcorrespondingauthor@text +Correspondence to: \icmlcorrespondingauthor@text. +\else +{\bf AUTHORERR: Missing \textbackslash{}icmlcorrespondingauthor.} +\fi + +\ \\ +\Notice@String +} +} +} + +%\makeatother + +\long\def\icmladdress#1{% + {\bf The \textbackslash{}icmladdress command is no longer used. See the example\_paper PDF .tex for usage of \textbackslash{}icmlauther and \textbackslash{}icmlaffiliation.} +} + +%% keywords as first class citizens +\def\icmlkeywords#1{% +% \ifdefined\isaccepted \else +% \par {\bf Keywords:} #1% +% \fi +% \ifdefined\nohyperref\else\ifdefined\hypersetup +% \hypersetup{pdfkeywords={#1}} +% \fi\fi +% \ifdefined\isaccepted \else +% \par {\bf Keywords:} #1% +% \fi + \ifdefined\nohyperref\else\ifdefined\hypersetup + \hypersetup{pdfkeywords={#1}} + \fi\fi +} + +% modification to natbib citations +\setcitestyle{authoryear,round,citesep={;},aysep={,},yysep={;}} + +% Redefinition of the abstract environment. +\renewenvironment{abstract} + {% +% Insert the ``appearing in'' copyright notice. +%\@copyrightspace +\centerline{\large\bf Abstract} + \vspace{-0.12in}\begin{quote}} + {\par\end{quote}\vskip 0.12in} + +% numbered section headings with different treatment of numbers + +\def\@startsection#1#2#3#4#5#6{\if@noskipsec \leavevmode \fi + \par \@tempskipa #4\relax + \@afterindenttrue +% Altered the following line to indent a section's first paragraph. +% \ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \@afterindentfalse\fi + \ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \fi + \if@nobreak \everypar{}\else + \addpenalty{\@secpenalty}\addvspace{\@tempskipa}\fi \@ifstar + {\@ssect{#3}{#4}{#5}{#6}}{\@dblarg{\@sict{#1}{#2}{#3}{#4}{#5}{#6}}}} + +\def\@sict#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth + \def\@svsec{}\else + \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname}\fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup #6\relax + \@hangfrom{\hskip #3\relax\@svsec.~}{\interlinepenalty \@M #8\par} + \endgroup + \csname #1mark\endcsname{#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}\else + \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname + {#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}}\fi + \@xsect{#5}} + +\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth + \def\@svsec{}\else + \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname\hskip 0.4em }\fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup #6\relax + \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par} + \endgroup + \csname #1mark\endcsname{#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}\else + \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname + {#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}}\fi + \@xsect{#5}} + +% section headings with less space above and below them +\def\thesection {\arabic{section}} +\def\thesubsection {\thesection.\arabic{subsection}} +\def\section{\@startsection{section}{1}{\z@}{-0.12in}{0.02in} + {\large\bf\raggedright}} +\def\subsection{\@startsection{subsection}{2}{\z@}{-0.10in}{0.01in} + {\normalsize\bf\raggedright}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-0.08in}{0.01in} + {\normalsize\sc\raggedright}} +\def\paragraph{\@startsection{paragraph}{4}{\z@}{1.5ex plus + 0.5ex minus .2ex}{-1em}{\normalsize\bf}} +\def\subparagraph{\@startsection{subparagraph}{5}{\z@}{1.5ex plus + 0.5ex minus .2ex}{-1em}{\normalsize\bf}} + +% Footnotes +\footnotesep 6.65pt % +\skip\footins 9pt +\def\footnoterule{\kern-3pt \hrule width 0.8in \kern 2.6pt } +\setcounter{footnote}{0} + +% Lists and paragraphs +\parindent 0pt +\topsep 4pt plus 1pt minus 2pt +\partopsep 1pt plus 0.5pt minus 0.5pt +\itemsep 2pt plus 1pt minus 0.5pt +\parsep 2pt plus 1pt minus 0.5pt +\parskip 6pt + +\leftmargin 2em \leftmargini\leftmargin \leftmarginii 2em +\leftmarginiii 1.5em \leftmarginiv 1.0em \leftmarginv .5em +\leftmarginvi .5em +\labelwidth\leftmargini\advance\labelwidth-\labelsep \labelsep 5pt + +\def\@listi{\leftmargin\leftmargini} +\def\@listii{\leftmargin\leftmarginii + \labelwidth\leftmarginii\advance\labelwidth-\labelsep + \topsep 2pt plus 1pt minus 0.5pt + \parsep 1pt plus 0.5pt minus 0.5pt + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii\advance\labelwidth-\labelsep + \topsep 1pt plus 0.5pt minus 0.5pt + \parsep \z@ \partopsep 0.5pt plus 0pt minus 0.5pt + \itemsep \topsep} +\def\@listiv{\leftmargin\leftmarginiv + \labelwidth\leftmarginiv\advance\labelwidth-\labelsep} +\def\@listv{\leftmargin\leftmarginv + \labelwidth\leftmarginv\advance\labelwidth-\labelsep} +\def\@listvi{\leftmargin\leftmarginvi + \labelwidth\leftmarginvi\advance\labelwidth-\labelsep} + +\abovedisplayskip 7pt plus2pt minus5pt% +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip 0pt plus3pt% +\belowdisplayshortskip 4pt plus3pt minus3pt% + +% Less leading in most fonts (due to the narrow columns) +% The choices were between 1-pt and 1.5-pt leading +\def\@normalsize{\@setsize\normalsize{11pt}\xpt\@xpt} +\def\small{\@setsize\small{10pt}\ixpt\@ixpt} +\def\footnotesize{\@setsize\footnotesize{10pt}\ixpt\@ixpt} +\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt} +\def\tiny{\@setsize\tiny{7pt}\vipt\@vipt} +\def\large{\@setsize\large{14pt}\xiipt\@xiipt} +\def\Large{\@setsize\Large{16pt}\xivpt\@xivpt} +\def\LARGE{\@setsize\LARGE{20pt}\xviipt\@xviipt} +\def\huge{\@setsize\huge{23pt}\xxpt\@xxpt} +\def\Huge{\@setsize\Huge{28pt}\xxvpt\@xxvpt} + +% Revised formatting for figure captions and table titles. +\newsavebox\newcaptionbox\newdimen\newcaptionboxwid + +\long\def\@makecaption#1#2{ + \vskip 10pt + \baselineskip 11pt + \setbox\@tempboxa\hbox{#1. #2} + \ifdim \wd\@tempboxa >\hsize + \sbox{\newcaptionbox}{\small\sl #1.~} + \newcaptionboxwid=\wd\newcaptionbox + \usebox\newcaptionbox {\footnotesize #2} +% \usebox\newcaptionbox {\small #2} + \else + \centerline{{\small\sl #1.} {\small #2}} + \fi} + +\def\fnum@figure{Figure \thefigure} +\def\fnum@table{Table \thetable} + +% Strut macros for skipping spaces above and below text in tables. +\def\abovestrut#1{\rule[0in]{0in}{#1}\ignorespaces} +\def\belowstrut#1{\rule[-#1]{0in}{#1}\ignorespaces} + +\def\abovespace{\abovestrut{0.20in}} +\def\aroundspace{\abovestrut{0.20in}\belowstrut{0.10in}} +\def\belowspace{\belowstrut{0.10in}} + +% Various personal itemization commands. +\def\texitem#1{\par\noindent\hangindent 12pt + \hbox to 12pt {\hss #1 ~}\ignorespaces} +\def\icmlitem{\texitem{$\bullet$}} + +% To comment out multiple lines of text. +\long\def\comment#1{} + + + + +%% Line counter (not in final version). Adapted from NIPS style file by Christoph Sawade + +% Vertical Ruler +% This code is, largely, from the CVPR 2010 conference style file +% ----- define vruler +\makeatletter +\newbox\icmlrulerbox +\newcount\icmlrulercount +\newdimen\icmlruleroffset +\newdimen\cv@lineheight +\newdimen\cv@boxheight +\newbox\cv@tmpbox +\newcount\cv@refno +\newcount\cv@tot +% NUMBER with left flushed zeros \fillzeros[] +\newcount\cv@tmpc@ \newcount\cv@tmpc +\def\fillzeros[#1]#2{\cv@tmpc@=#2\relax\ifnum\cv@tmpc@<0\cv@tmpc@=-\cv@tmpc@\fi +\cv@tmpc=1 % +\loop\ifnum\cv@tmpc@<10 \else \divide\cv@tmpc@ by 10 \advance\cv@tmpc by 1 \fi + \ifnum\cv@tmpc@=10\relax\cv@tmpc@=11\relax\fi \ifnum\cv@tmpc@>10 \repeat +\ifnum#2<0\advance\cv@tmpc1\relax-\fi +\loop\ifnum\cv@tmpc<#1\relax0\advance\cv@tmpc1\relax\fi \ifnum\cv@tmpc<#1 \repeat +\cv@tmpc@=#2\relax\ifnum\cv@tmpc@<0\cv@tmpc@=-\cv@tmpc@\fi \relax\the\cv@tmpc@}% +% \makevruler[][][][][] +\def\makevruler[#1][#2][#3][#4][#5]{ + \begingroup\offinterlineskip + \textheight=#5\vbadness=10000\vfuzz=120ex\overfullrule=0pt% + \global\setbox\icmlrulerbox=\vbox to \textheight{% + { + \parskip=0pt\hfuzz=150em\cv@boxheight=\textheight + \cv@lineheight=#1\global\icmlrulercount=#2% + \cv@tot\cv@boxheight\divide\cv@tot\cv@lineheight\advance\cv@tot2% + \cv@refno1\vskip-\cv@lineheight\vskip1ex% + \loop\setbox\cv@tmpbox=\hbox to0cm{ % side margin + \hfil {\hfil\fillzeros[#4]\icmlrulercount} + }% + \ht\cv@tmpbox\cv@lineheight\dp\cv@tmpbox0pt\box\cv@tmpbox\break + \advance\cv@refno1\global\advance\icmlrulercount#3\relax + \ifnum\cv@refno<\cv@tot\repeat + } + } + \endgroup +}% +\makeatother +% ----- end of vruler + + +% \makevruler[][][][][] +\def\icmlruler#1{\makevruler[12pt][#1][1][3][\textheight]\usebox{\icmlrulerbox}} +\AddToShipoutPicture{% +\icmlruleroffset=\textheight +\advance\icmlruleroffset by 5.2pt % top margin + \color[rgb]{.7,.7,.7} + \ifdefined\isaccepted \else + \AtTextUpperLeft{% + \put(\LenToUnit{-35pt},\LenToUnit{-\icmlruleroffset}){%left ruler + \icmlruler{\icmlrulercount}} +% \put(\LenToUnit{1.04\textwidth},\LenToUnit{-\icmlruleroffset}){%right ruler +% \icmlruler{\icmlrulercount}} + } + \fi +} +\endinput diff --git a/docs/ICML_workshop/icml2023/icml_numpapers.pdf b/docs/ICML_workshop/icml2023/icml_numpapers.pdf new file mode 100644 index 0000000..98d2167 Binary files /dev/null and b/docs/ICML_workshop/icml2023/icml_numpapers.pdf differ diff --git a/docs/binary-iris-architecture.png b/docs/binary-iris-architecture.png new file mode 100644 index 0000000..b1d73a7 Binary files /dev/null and b/docs/binary-iris-architecture.png differ diff --git a/docs/db-net.png b/docs/db-net.png new file mode 100644 index 0000000..de5e832 Binary files /dev/null and b/docs/db-net.png differ diff --git a/docs/db.bib b/docs/db.bib new file mode 100644 index 0000000..f8b8c45 --- /dev/null +++ b/docs/db.bib @@ -0,0 +1,335 @@ +@misc{granmo18, + doi = {10.48550/ARXIV.1804.01508}, + + url = {https://arxiv.org/abs/1804.01508}, + + author = {Granmo, Ole-Christoffer}, + + keywords = {Artificial Intelligence (cs.AI), Computer Vision and Pattern Recognition (cs.CV), Machine Learning (cs.LG), FOS: Computer and information sciences, FOS: Computer and information sciences}, + + title = {The {T}setlin Machine -- A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic}, + + publisher = {arXiv}, + + year = {2018}, + + copyright = {arXiv.org perpetual, non-exclusive license} +} + +@misc{noisy-xor-dataset, + author = {Granmo, Ole-Christoffer}, + title = {The noisy {XOR} dataset}, + howpublished = {GitHub repository}, + url = {https://github.com/cair/TsetlinMachine} +} + +@misc{binary-iris-dataset, + author = {Granmo, Ole-Christoffer}, + title = {The binary Iris dataset}, + howpublished = {GitHub repository}, + url = {https://github.com/cair/TsetlinMachine} +} + +@inproceedings{ + Liu2020On, + title={On the Variance of the Adaptive Learning Rate and Beyond}, + author={Liyuan Liu and Haoming Jiang and Pengcheng He and Weizhu Chen and Xiaodong Liu and Jianfeng Gao and Jiawei Han}, + booktitle={International Conference on Learning Representations}, + year={2020}, + url={https://openreview.net/forum?id=rkgz2aEKDr} +} + +@article{DBLP:journals/corr/BengioLC13, + author = {Yoshua Bengio and Nicholas L{\'{e}}onard and Aaron C. Courville}, + title = {Estimating or Propagating Gradients Through Stochastic Neurons for + Conditional Computation}, + journal = {CoRR}, + volume = {abs/1308.3432}, + year = {2013}, + url = {http://arxiv.org/abs/1308.3432}, + eprinttype = {arXiv}, + eprint = {1308.3432}, + timestamp = {Mon, 13 Aug 2018 16:47:35 +0200}, + biburl = {https://dblp.org/rec/journals/corr/BengioLC13.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{rumelhart1986learning, + title={Learning representations by back-propagating errors}, + author={Rumelhart, David E and Hinton, Geoffrey E and Williams, Ronald J}, + journal={Nature}, + volume={323}, + number={6088}, + pages={533--536}, + year={1986}, + publisher={Nature Publishing Group} +} + +@inproceedings{10.5555/3104322.3104425, + author = {Nair, Vinod and Hinton, Geoffrey E.}, + title = {Rectified Linear Units Improve Restricted Boltzmann Machines}, + year = {2010}, + isbn = {9781605589077}, + publisher = {Omnipress}, + address = {Madison, WI, USA}, + abstract = {Restricted Boltzmann machines were developed using binary stochastic hidden units. These can be generalized by replacing each binary unit by an infinite number of copies that all have the same weights but have progressively more negative biases. The learning and inference rules for these "Stepped Sigmoid Units" are unchanged. They can be approximated efficiently by noisy, rectified linear units. Compared with binary units, these units learn features that are better for object recognition on the NORB dataset and face verification on the Labeled Faces in the Wild dataset. Unlike binary units, rectified linear units preserve information about relative intensities as information travels through multiple layers of feature detectors.}, + booktitle = {Proceedings of the 27th International Conference on International Conference on Machine Learning}, + pages = {807–814}, + numpages = {8}, + location = {Haifa, Israel}, + series = {ICML'10} +} + +@inproceedings{10.5555/3157382.3157557, + author = {Hubara, Itay and Courbariaux, Matthieu and Soudry, Daniel and El-Yaniv, Ran and Bengio, Yoshua}, + title = {Binarized Neural Networks}, + year = {2016}, + isbn = {9781510838819}, + publisher = {Curran Associates Inc.}, + address = {Red Hook, NY, USA}, + abstract = {We introduce a method to train Binarized Neural Networks (BNNs) - neural networks with binary weights and activations at run-time. At train-time the binary weights and activations are used for computing the parameter gradients. During the forward pass, BNNs drastically reduce memory size and accesses, and replace most arithmetic operations with bit-wise operations, which is expected to substantially improve power-efficiency. To validate the effectiveness of BNNs, we conducted two sets of experiments on the Torch7 and Theano frameworks. On both, BNNs achieved nearly state-of-the-art results over the MNIST, CIFAR-10 and SVHN datasets. We also report our preliminary results on the challenging ImageNet dataset. Last but not least, we wrote a binary matrix multiplication GPU kernel with which it is possible to run our MNIST BNN 7 times faster than with an unoptimized GPU kernel, without suffering any loss in classification accuracy. The code for training and running our BNNs is available on-line.}, + booktitle = {Proceedings of the 30th International Conference on Neural Information Processing Systems}, + pages = {4114–4122}, + numpages = {9}, + location = {Barcelona, Spain}, + series = {NIPS'16} +} + +@article{JMLR:v15:srivastava14a, + author = {Nitish Srivastava and Geoffrey Hinton and Alex Krizhevsky and Ilya Sutskever and Ruslan Salakhutdinov}, + title = {Dropout: A Simple Way to Prevent Neural Networks from Overfitting}, + journal = {Journal of Machine Learning Research}, + year = {2014}, + volume = {15}, + number = {56}, + pages = {1929--1958}, + url = {http://jmlr.org/papers/v15/srivastava14a.html} +} + +@inproceedings{10.5555/2969442.2969588, + author = {Courbariaux, Matthieu and Bengio, Yoshua and David, Jean-Pierre}, + title = {BinaryConnect: Training Deep Neural Networks with Binary Weights during Propagations}, + year = {2015}, + publisher = {MIT Press}, + address = {Cambridge, MA, USA}, + abstract = {Deep Neural Networks (DNN) have achieved state-of-the-art results in a wide range of tasks, with the best results obtained with large training sets and large models. In the past, GPUs enabled these breakthroughs because of their greater computational speed. In the future, faster computation at both training and test time is likely to be crucial for further progress and for consumer applications on low-power devices. As a result, there is much interest in research and development of dedicated hardware for Deep Learning (DL). Binary weights, i.e., weights which are constrained to only two possible values (e.g. -1 or 1), would bring great benefits to specialized DL hardware by replacing many multiply-accumulate operations by simple accumulations, as multipliers are the most space and power-hungry components of the digital implementation of neural networks. We introduce BinaryConnect, a method which consists in training a DNN with binary weights during the forward and backward propagations, while retaining precision of the stored weights in which gradients are accumulated. Like other dropout schemes, we show that BinaryConnect acts as regularizer and we obtain near state-of-the-art results with BinaryConnect on the permutation-invariant MNIST, CIFAR-10 and SVHN.}, + booktitle = {Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 2}, + pages = {3123–3131}, + numpages = {9}, + location = {Montreal, Canada}, + series = {NIPS'15} +} + +@ARTICLE {9026948, + author = {E. Wang and J. J. Davis and P. K. Cheung and G. A. Constantinides}, + journal = {IEEE Transactions on Computers}, + title = {LUTNet: Learning FPGA Configurations for Highly Efficient Neural Network Inference}, + year = {2020}, + volume = {69}, + number = {12}, + issn = {1557-9956}, + pages = {1795-1808}, + abstract = {Research has shown that deep neural networks contain significant redundancy, and thus that high classification accuracy can be achieved even when weights and activations are quantized down to binary values. Network binarization on FPGAs greatly increases area efficiency by replacing resource-hungry multipliers with lightweight XNOR gates. However, an FPGA's fundamental building block, the K-LUT, is capable of implementing far more than an XNOR: it can perform any K-input Boolean operation. Inspired by this observation, we propose LUTNet, an end-to-end hardware-software framework for the construction of area-efficient FPGA-based neural network accelerators using the native LUTs as inference operators. We describe the realization of both unrolled and tiled LUTNet architectures, with the latter facilitating smaller, less power-hungry deployment over the former while sacrificing area and energy efficiency along with throughput. For both varieties, we demonstrate that the exploitation of LUT flexibility allows for far heavier pruning than possible in prior works, resulting in significant area savings while achieving comparable accuracy. Against the state-of-the-art binarized neural network implementation, we achieve up to twice the area efficiency for several standard network models when inferencing popular datasets. We also demonstrate that even greater energy efficiency improvements are obtainable.}, + keywords = {table lookup;deep learning;field programmable gate arrays;neural networks;logic gates;random access memory}, + doi = {10.1109/TC.2020.2978817}, + publisher = {IEEE Computer Society}, + address = {Los Alamitos, CA, USA}, + month = {dec} +} + +@InProceedings{10.1007/978-3-319-46493-0_32, + author="Rastegari, Mohammad and Ordonez, Vicente and Redmon, Joseph and Farhadi, Ali", editor="Leibe, Bastian and Matas, Jiri and Sebe, Nicu and Welling, Max", + title="XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks", + booktitle="Computer Vision -- ECCV 2016", + year="2016", + publisher="Springer International Publishing", + address="Cham", + pages="525--542", + abstract="We propose two efficient approximations to standard convolutional neural networks: Binary-Weight-Networks and XNOR-Networks. In Binary-Weight-Networks, the filters are approximated with binary values resulting in 32{\$}{\$}{\backslash}times {\$}{\$}{\texttimes}memory saving. In XNOR-Networks, both the filters and the input to convolutional layers are binary. XNOR-Networks approximate convolutions using primarily binary operations. This results in 58{\$}{\$}{\backslash}times {\$}{\$}{\texttimes}faster convolutional operations (in terms of number of the high precision operations) and 32{\$}{\$}{\backslash}times {\$}{\$}{\texttimes}memory savings. XNOR-Nets offer the possibility of running state-of-the-art networks on CPUs (rather than GPUs) in real-time. Our binary networks are simple, accurate, efficient, and work on challenging visual tasks. We evaluate our approach on the ImageNet classification task. The classification accuracy with a Binary-Weight-Network version of AlexNet is the same as the full-precision AlexNet. We compare our method with recent network binarization methods, BinaryConnect and BinaryNets, and outperform these methods by large margins on ImageNet, more than {\$}{\$}16{\backslash},{\backslash}{\%}{\$}{\$}16{\%}in top-1 accuracy. Our code is available at: http://allenai.org/plato/xnornet.", + isbn="978-3-319-46493-0" +} + +@article{QIN2020107281, + title = {Binary neural networks: A survey}, + journal = {Pattern Recognition}, + volume = {105}, + pages = {107281}, + year = {2020}, + issn = {0031-3203}, + doi = {https://doi.org/10.1016/j.patcog.2020.107281}, + url = {https://www.sciencedirect.com/science/article/pii/S0031320320300856}, + author = {Haotong Qin and Ruihao Gong and Xianglong Liu and Xiao Bai and Jingkuan Song and Nicu Sebe}, + keywords = {Binary neural network, Deep learning, Model compression, Network quantization, Model acceleration}, + abstract = {The binary neural network, largely saving the storage and computation, serves as a promising technique for deploying deep models on resource-limited devices. However, the binarization inevitably causes severe information loss, and even worse, its discontinuity brings difficulty to the optimization of the deep network. To address these issues, a variety of algorithms have been proposed, and achieved satisfying progress in recent years. In this paper, we present a comprehensive survey of these algorithms, mainly categorized into the native solutions directly conducting binarization, and the optimized ones using techniques like minimizing the quantization error, improving the network loss function, and reducing the gradient error. We also investigate other practical aspects of binary neural networks such as the hardware-friendly design and the training tricks. Then, we give the evaluation and discussions on different tasks, including image classification, object detection and semantic segmentation. Finally, the challenges that may be faced in future research are prospected.} +} + +@inproceedings{ + dong2018neural, + title={Neural Logic Machines}, + author={Honghua Dong and Jiayuan Mao and Tian Lin and Chong Wang and Lihong Li and Denny Zhou}, + booktitle={International Conference on Learning Representations}, + year={2019}, + url={https://openreview.net/forum?id=B1xY-hRctX}, +} + +@article{10.5555/3241691.3241692, + author = {Evans, Richard and Grefenstette, Edward}, + title = {Learning Explanatory Rules from Noisy Data}, + year = {2018}, + issue_date = {January 2018}, + publisher = {AI Access Foundation}, + address = {El Segundo, CA, USA}, + volume = {61}, + number = {1}, + issn = {1076-9757}, + abstract = {Artificial Neural Networks are powerful function approximators capable of modelling solutions to a wide variety of problems, both supervised and unsupervised. As their size and expressivity increases, so too does the variance of the model, yielding a nearly ubiquitous over_tting problem. Although mitigated by a variety of model regularisation methods, the common cure is to seek large amounts of training data--which is not necessarily easily obtained--that sufficiently approximates the data distribution of the domain we wish to test on. In contrast, logic programming methods such as Inductive Logic Programming offer an extremely data-efficient process by which models can be trained to reason on symbolic domains. However, these methods are unable to deal with the variety of domains neural networks can be applied to: they are not robust to noise in or mislabelling of inputs, and perhaps more importantly, cannot be applied to non-symbolic domains where the data is ambiguous, such as operating on raw pixels. In this paper, we propose a Differentiable Inductive Logic framework, which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with. Furthermore, as it is trained by backpropagation against a likelihood objective, it can be hybridised by connecting it with neural networks over ambiguous data in order to be applied to domains which ILP cannot address, while providing data efficiency and generalisation beyond what neural networks on their own can achieve.}, + journal = {J. Artif. Int. Res.}, + month = {jan}, + pages = {1–64}, + numpages = {64} +} + +@Book{BreiFrieStonOlsh84, + Title = {Classification and Regression Trees}, + Author = {Leo Breiman and Jerome Friedman and Charles J. Stone and and R.A. Olshen}, + Publisher = {Chapman and Hall/CRC}, + Year = {1984} +} + +@INPROCEEDINGS{598994, + author={Tin Kam Ho}, + booktitle={Proceedings of 3rd International Conference on Document Analysis and Recognition}, + title={Random decision forests}, + year={1995}, + volume={1}, + number={}, + pages={278-282 vol.1}, + doi={10.1109/ICDAR.1995.598994}} + +@book{koza1992genetic, + title={Genetic Programming: On the Programming of Computers by Means of Natural Selection}, + author={Koza, J.R.}, + isbn={9780262111706}, + lccn={92025785}, + series={A Bradford book}, + url={https://books.google.co.uk/books?id=Bhtxo60BV0EC}, + year={1992}, + publisher={Bradford} +} + +@inproceedings{NEURIPS2019_d8c24ca8, + author = {Cuturi, Marco and Teboul, Olivier and Vert, Jean-Philippe}, + booktitle = {Advances in Neural Information Processing Systems}, + editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett}, + pages = {}, + publisher = {Curran Associates, Inc.}, + title = {Differentiable Ranking and Sorting using Optimal Transport}, + url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/d8c24ca8f23c562a5600876ca2a550ce-Paper.pdf}, + volume = {32}, + year = {2019} +} + +@article{VANKRIEKEN2022103602, + title = {Analyzing Differentiable Fuzzy Logic Operators}, + journal = {Artificial Intelligence}, + volume = {302}, + pages = {103602}, + year = {2022}, + issn = {0004-3702}, + doi = {https://doi.org/10.1016/j.artint.2021.103602}, + url = {https://www.sciencedirect.com/science/article/pii/S0004370221001533}, + author = {Emile {van Krieken} and Erman Acar and Frank {van Harmelen}}, + keywords = {Fuzzy logic, Neural-symbolic AI, Learning with constraints}, + abstract = {The AI community is increasingly putting its attention towards combining symbolic and neural approaches, as it is often argued that the strengths and weaknesses of these approaches are complementary. One recent trend in the literature is weakly supervised learning techniques that employ operators from fuzzy logics. In particular, these use prior background knowledge described in such logics to help the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks, this background knowledge can be added to regular loss functions, hence making reasoning a part of learning. We study, both formally and empirically, how a large collection of logical operators from the fuzzy logic literature behave in a differentiable learning setting. We find that many of these operators, including some of the most well-known, are highly unsuitable in this setting. A further finding concerns the treatment of implication in these fuzzy logics, and shows a strong imbalance between gradients driven by the antecedent and the consequent of the implication. Furthermore, we introduce a new family of fuzzy implications (called sigmoidal implications) to tackle this phenomenon. Finally, we empirically show that it is possible to use Differentiable Fuzzy Logics for semi-supervised learning, and compare how different operators behave in practice. We find that, to achieve the largest performance improvement over a supervised baseline, we have to resort to non-standard combinations of logical operators which perform well in learning, but no longer satisfy the usual logical laws.} +} + +@phdthesis{DBLP:phd/basesearch/Payani20, + author = {Ali Payani}, + title = {Differentiable neural logic networks and their application onto inductive + logic programming}, + school = {Georgia Institute of Technology, Atlanta, GA, {USA}}, + year = {2020}, + url = {https://hdl.handle.net/1853/62833}, + timestamp = {Wed, 04 May 2022 13:00:04 +0200}, + biburl = {https://dblp.org/rec/phd/basesearch/Payani20.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{Granmo2019TheCT, + title={The Convolutional Tsetlin Machine}, + author={Ole-Christoffer Granmo and Sondre Glimsdal and Lei Jiao and Morten Goodwin Olsen and Christian Walter Peter Omlin and Geir Thore Berge}, + journal={ArXiv}, + year={2019}, + volume={abs/1905.09688} +} + +@software{flax2020github, + author = {Jonathan Heek and Anselm Levskaya and Avital Oliver and Marvin Ritter and Bertrand Rondepierre and Andreas Steiner and Marc van {Z}ee}, + title = {{F}lax: A neural network library and ecosystem for {JAX}}, + url = {http://github.com/google/flax}, + version = {0.6.8}, + year = {2023}, +} + +@software{jax2018github, + author = {James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander{P}las and Skye Wanderman-{M}ilne and Qiao Zhang}, + title = {{JAX}: composable transformations of {P}ython+{N}um{P}y programs}, + url = {http://github.com/google/jax}, + version = {0.3.13}, + year = {2018}, +} + +@ARTICLE{726791, + author={Le{C}un, Y. and Bottou, L. and Bengio, Y. and Haffner, P.}, + journal={Proceedings of the IEEE}, + title={Gradient-based learning applied to document recognition}, + year={1998}, + volume={86}, + number={11}, + pages={2278-2324}, + doi={10.1109/5.726791}} + +@article{KIWIEL2005214, + title = {On {F}loyd and {R}ivest's {SELECT} algorithm}, + journal = {Theoretical Computer Science}, + volume = {347}, + number = {1}, + pages = {214-238}, + year = {2005}, + issn = {0304-3975}, + doi = {https://doi.org/10.1016/j.tcs.2005.06.032}, + url = {https://www.sciencedirect.com/science/article/pii/S0304397505004081}, + author = {Krzysztof C. Kiwiel}, + keywords = {Selection, Medians, Partitioning, Computational complexity}, + abstract = {We show that several versions of Floyd and Rivest's algorithm SELECT for finding the kth smallest of n elements require at most n+min{k,n-k}+o(n) comparisons on average and with high probability. This rectifies the analysis of Floyd and Rivest, and extends it to the case of nondistinct elements. Our computational results confirm that SELECT may be the best algorithm in practice.} +} + +@inproceedings{ + petersen2022monotonic, + title={Monotonic Differentiable Sorting Networks}, + author={Felix Petersen and Christian Borgelt and Hilde Kuehne and Oliver Deussen}, + booktitle={International Conference on Learning Representations}, + year={2022}, + url={https://openreview.net/forum?id=IcUWShptD7d} +} + +@inproceedings{ + grover2018stochastic, + title={Stochastic Optimization of Sorting Networks via Continuous Relaxations}, + author={Aditya Grover and Eric Wang and Aaron Zweig and Stefano Ermon}, + booktitle={International Conference on Learning Representations}, + year={2019}, + url={https://openreview.net/forum?id=H1eSS3CcKX}, +} + +@inproceedings{NEURIPS2022_0d3496dd, + author = {Petersen, Felix and Borgelt, Christian and Kuehne, Hilde and Deussen, Oliver}, + booktitle = {Advances in Neural Information Processing Systems}, + editor = {S. Koyejo and S. Mohamed and A. Agarwal and D. Belgrave and K. Cho and A. Oh}, + pages = {2006--2018}, + publisher = {Curran Associates, Inc.}, + title = {Deep Differentiable Logic Gate Networks}, + url = {https://proceedings.neurips.cc/paper_files/paper/2022/file/0d3496dd0cec77a999c98d35003203ca-Paper-Conference.pdf}, + volume = {35}, + year = {2022} +} \ No newline at end of file diff --git a/docs/db.pdf b/docs/db.pdf new file mode 100644 index 0000000..f0284ed Binary files /dev/null and b/docs/db.pdf differ diff --git a/docs/db.tex b/docs/db.tex new file mode 100644 index 0000000..58d3e55 --- /dev/null +++ b/docs/db.tex @@ -0,0 +1,755 @@ + +\documentclass{article} % For LaTeX2e +\usepackage{iclr2021_conference,times} + +% Optional math commands from https://github.com/goodfeli/dlbook_notation. +\input{math_commands.tex} + +\usepackage{hyperref} +\usepackage{url} +\usepackage{amsthm} +\usepackage{amssymb} +\usepackage{graphicx} +\usepackage{comment} +\usepackage{xcolor} +\usepackage{listings} + +\lstset{basicstyle=\ttfamily\tiny} +\lstdefinestyle{mystyle}{ + keywordstyle=\bfseries, + keywords={ge,return,def,not,xor,ne}, +} +\lstset{breaklines=true} + + +\title{$\partial\mathbb{B}$ nets: learning discrete functions by\\gradient descent} + +% Authors must not appear in the submitted version. They should be hidden +% as long as the \iclrfinalcopy macro remains commented out below. +% Non-anonymous submissions will be rejected without review. + +\author{Ian Wright\thanks{wrighti@acm.org}} + +% The \author macro works with any number of authors. There are two commands +% used to separate the names and addresses of multiple authors: \And and \AND. +% +% Using \And between authors leaves it to \LaTeX{} to determine where to break +% the lines. Using \AND forces a linebreak at that point. So, if \LaTeX{} +% puts 3 of 4 authors names on the first line, and the last on the second +% line, try using \AND instead of \And before the third author name. + +\newcommand{\fix}{\marginpar{FIX}} +\newcommand{\new}{\marginpar{NEW}} + +\newtheorem{theorem}{Theorem} +\newtheorem*{definition}{Definition} +\newtheorem{prop}{Proposition} +\newtheorem{lemma}{Lemma} + +\makeatletter +\newcommand{\tleft}{\mathrel\triangleleft} +\newcommand{\tright}{\mathrel\triangleright} +\DeclareRobustCommand{\btleft}{\mathrel{\mathpalette\btlr@\blacktriangleleft}} +\DeclareRobustCommand{\btright}{\mathrel{\mathpalette\btlr@\blacktriangleright}} + +\newcommand{\btlr@}[2]{% + \begingroup + \sbox\z@{$\m@th#1\triangleright$}% + \sbox\tw@{\resizebox{1.1\wd\z@}{1.1\ht\z@}{\raisebox{\depth}{$\m@th#1\mkern-1mu#2$}}}% + \ht\tw@=\ht\z@ \dp\tw@=\dp\z@ \wd\tw@=\wd\z@ + \copy\tw@ + \endgroup +} + +\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission. +\begin{document} + +\maketitle + +\begin{abstract} + $\partial\mathbb{B}$ nets are differentiable neural networks that learn discrete boolean-valued functions by gradient descent. $\partial\mathbb{B}$ nets have two semantically equivalent aspects: a differentiable soft-net, with real weights, and a non-differentiable hard-net, with boolean weights. We train the soft-net by backpropagation and then `harden' the learned weights to yield boolean weights that bind with the hard-net. The result is a learned discrete function. `Hardening' involves no loss of accuracy, unlike existing approaches to neural network binarization. Preliminary experiments demonstrate that $\partial\mathbb{B}$ nets achieve comparable performance on standard machine learning problems yet are compact (due to 1-bit weights) and interpretable (due to the logical nature of the learnt functions). +\end{abstract} + +\section{Introduction} + +Neural networks are differentiable functions with weights represented by machine floats. Networks are trained by gradient descent in weight-space, where the direction of descent minimises loss. The gradients are efficiently calculated by the backpropagation algorithm \citep{rumelhart1986learning}. This overall approach has led to tremendous advances in machine learning. + +However, there are drawbacks. First, differentiability means we cannot directly learn discrete functions, such as logical predicates. In consequence, what a network has learned is difficult to interpret and verify. Second, representing weights as machine floats enables time-efficient training but at the cost of memory-inefficient models. For example, network quantisation techniques (see \cite{QIN2020107281}) demonstrate that full 64 or 32-bit precision weights are often unnecessary for final predictive performance, although there is a trade-off. + +A standard approach to mitigate these drawbacks is to approximate discrete functions by defining continuous relaxations. This paper explores a different approach: we define differentiable functions that `harden', without approximation, to discrete functions. Specifically, we define $\partial \mathbb{B}$ nets that have two equivalent aspects: a {\em soft-net}, which is a differentiable real-valued function, and a {\em hard-net}, which is a non-differentiable, discrete function. Both aspects are semantically equivalent. We train the soft-net as normal, using backpropagation, then `harden' the learned weights to boolean values, which we then bind with the hard-net to yield a discrete function with identical predictive performance (see figure \ref{fig:main-idea}). In consequence, interpreting and verifying a $\partial \mathbb{B}$ net is relatively less difficult. And boolean-valued, 1-bit weights significantly increase the memory-efficiency of trained models. + +The main contributions of this work are (i) defining novel activation functions that `harden' to semantically equivalent discrete functions, (ii) defining novel network architectures to effectively learn discrete functions that solve multi-class classification problems, and (iii) experiments that demonstrate $\partial \mathbb{B}$ nets compete with existing approaches in terms of predictive performance yet yield compact models. + +Section \ref{sec:related-work} discusses related work, section \ref{sec:db-nets} defines $\partial\mathbb{B}$ nets, section \ref{sec:experiments} presents experimental results, and section \ref{sec:conclusion} concludes. + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{db-net.png} + \caption{{\em Learning discrete functions with a $\partial\mathbb{B}$ net.} A $\partial \mathbb{B}$ net specifies (i) a differentiable neural network that is hard-equivalent to (ii) a non-differentiable discrete function. The neural network is trained as normal with backpropagation to yield a set of real weights. The real weights are hardened to boolean values and then bound with the discrete function. The result is a learned discrete function that performs identically to the trained network.} + \label{fig:main-idea} +\end{figure} + +\section{Related work}\label{sec:related-work} + +Methods that learn discrete boolean functions can be broadly categorized as either non-differentiable or differentiable. + +Non-differentiable approaches include boolean-valued decision trees \citep{BreiFrieStonOlsh84}, random forests \citep{598994}, genetic programming \citep{koza1992genetic} and, more recently, Tsetlin machines \cite{granmo18}. Tsetlin machines represent propositional formulae by collections of simple automata with integer weights optimised by positive and negative feedback defined in terms of a hard threshold function. These models directly represent boolean decisions and therefore are easier to interpret compared to deep neural networks. However, they tend to perform less well, compared to differentiable approaches such as deep learning, on large volumes of high-dimensional data (e.g. NLP, images and audio) without manual feature engineering, although Tsetlin machines show promise on such tasks \citep{Granmo2019TheCT}. + +Differentiable approaches that learn boolean functions include (i) systems that integrate rule-based reasoning with neural components, and (ii) binarization techniques that quantize neural networks by converting real-valued weights and activations to binary values. For example, differentiable inductive logic programming \citep{10.5555/3241691.3241692}, neural logic machines \citep{dong2018neural} +and differentiable neural logic networks \cite{DBLP:phd/basesearch/Payani20} learn first-order logic rules using gradient descent. These systems combine the benefits of logical inference and interpretability with end-to-end differentiability. However, they rely on combinatoric enumeration of rulesets and therefore do not scale to large datasets. The technique of network binarization aims to significantly reduce model size and inference costs while maintaining predictive accuracy. Binarization reduces a real-valued neural network to a binary network where nonlinear activation functions are replaced by boolean majority functions. For example, BinaryConnect \citep{10.5555/2969442.2969588}, XNOR-Net \citep{10.1007/978-3-319-46493-0_32}, and LUTNet \citep{9026948}, optimize a continuous relaxation or approximation of the binary net during training. However, binary-valued functions are intrinsically non-differentiable and therefore training by gradient descent is challenging. Plus, binarization throws away information, which reduces accuracy \citep{QIN2020107281}. + +The design-space of algorithms that learn boolean functions is large, with various trade-offs. In this paper we investigate an under-explored area of differentiable nets that are semantically equivalent, without approximation or loss, to an arbitrarily complex boolean function. We aim to combine the benefits of deep neural networks trained by gradient descent with the efficiency, interpretability and logical bias of boolean functions -- but without loss of accuracy. + +\section{$\partial\mathbb{B}$ nets}\label{sec:db-nets} + +A $\partial \mathbb{B}$ net has two aspects, a soft-net and a hard-net. Both nets use bits to represent transitory values and learnable weights, but a soft-net uses soft-bits and a hard-net uses hard-bits. + +\begin{definition}[Soft-bits and hard-bits] +A {\em soft-bit} is a real value in the range $[0,1]$ and a {\em hard-bit} is a boolean value from the set $\{0,1\}$. A soft-bit, $x$, is {\em high} if $x>1/2$, otherwise it is {\em low}. +\end{definition} + +A hardening function converts soft-bits to hard-bits. + +\begin{definition}[Hardening] +The {\em hardening} function, $\operatorname{harden}(x_{1}, \dots, x_{n}) = [f(x_{1}), \dots, f(x_{n})]$, converts soft-bits to hard-bits, where +\begin{equation*} +f(x) = +\begin{cases} +1 & \text{if } x > 1/2 \\ +0 & \text{otherwise.} +\end{cases} +\end{equation*} +\end{definition} + +The soft-bit value $1/2$ is therefore a threshold. Above this threshold the soft-bit represents $\text{True}$, otherwise it represents $\text{False}$. + +A soft-net is any differentiable function, $f$, that `hardens' to a semantically equivalent discrete function, $g$. For example, if $f(x) = 1 - x$, where $x \in [0,1]$, and $g(y) = \neg y$, where $y \in \{0,1\}$ then: if $x$ is high (resp. low) then both $f(x)$ and $g(\operatorname{harden}(x))$ are low (resp. high). In other words, $f$ is hard-equivalent to boolean negation. More generally: + +\begin{definition}[Hard-equivalence] + A function, $f: [0,1]^n \rightarrow [0,1]^m$, is {\em hard-equivalent} to a discrete function, $g: \{1,0\}^n \rightarrow \{1,0\}^m$, if + \begin{equation*} + \operatorname{harden}(f({\bf x})) = g(\operatorname{harden}({\bf x})) + \end{equation*} + for all ${\bf x} \in \{(x_{1}, \dots, x_{n}) ~|~ x_{i} \in [0,1] \setminus \{1/2\}\}$. For shorthand write $f \btright g$. +\end{definition} + +Neural networks are typically composed of nonlinear activation functions (for representational generality) that are strictly monotonic (so gradients always exist that link changes in inputs to outputs without local minima) and smooth (so gradients reliably represent the local loss surface). However, activation functions that are monotonic but not strictly (so some gradients are zero) and differentiable almost everywhere (so some gradients are undefined) can also work, e.g. RELU \citep{10.5555/3104322.3104425}. $\partial \mathbb{B}$ nets are composed from `activation' functions that also satisfy these properties plus the additional property of hard-equivalence to a boolean function (and natural generalisations). We now turn to specifying the kind of `activation' functions used by $\partial \mathbb{B}$ nets. + +\begin{figure}[t!] + \centering + \includegraphics[trim=0pt 0pt 0pt 0pt, clip, width=1.0\textwidth]{logic-gates.png} + \caption{{\em Gradient-rich versus gradient-sparse differentiable boolean functions.} Each column contains contour plots of functions $f(x,y)$ that are hard-equivalent to a boolean function (one of $\neg(x \oplus y)$, $x \wedge y$, $x \vee y$, or $x \Rightarrow y$). Every function is continuous and differentiable almost everywhere (white lines indicate non-continuous derivatives). The upper plots are gradient-sparse, where vertical and horizontal contours indicate the function is constant with respect to one of its inputs, i.e. $\partial f/\partial y = 0$ or $\partial f/\partial x = 0$. The lower plots are gradient-rich, where the curved contours indicate the function always varies with respect to any of its inputs, i.e. $\partial f/\partial y \neq 0$ and $\partial f/\partial x \neq 0$. $\partial \mathbb{B}$ nets use gradient-rich functions to ensure that error is always backpropagated to all inputs.} + \label{fig:gradient-rich} +\end{figure} + +\subsection{Learning to negate} + +Say we aim to learn to negate a boolean value, $x$, or leave it unaltered. Represent this decision by a boolean weight, $w$, where low $w$ means negate and high $w$ means do not negate. The boolean function that meets this requirement is $\neg(x \oplus w)$. However, this function is not differentiable. Define the differentiable function, + \begin{equation*} + \begin{aligned} + \partial_{\neg}: [0, 1]^{2} &\to [0,1], \\ + (w, x) &\mapsto 1 - w + x (2w - 1)\text{,} + \end{aligned} + \end{equation*} +where $\partial_{\neg}(w, x) \btright \neg(x \oplus w)$ (see proposition \ref{prop:not}). + +There are many kinds of differentiable fuzzy logic operators (see \cite{VANKRIEKEN2022103602} for a review). So why this functional form? Product logics, where $f(x,y) = x y$ is as a soft version of $x \wedge y$, although hard-equivalent at extreme values, e.g. $f(1,1)=1$ and $f(0,1)=0$, are not hard-equivalent at intermediate values, e.g. $f(0.6, 0.6) = 0.36$, which hardens to $\operatorname{False}$ not $\operatorname{True}$. G\"{o}del-style $\operatorname{min}$ and $\operatorname{max}$ functions, although hard-equivalent over the entire soft-bit range, i.e. $\operatorname{min}(x,y) \btright x \wedge y$ and $\operatorname{max}(x,y) \btright x \vee y$, are gradient-sparse in the sense that their outputs do not always vary when any input changes, e.g. $\frac{\partial}{\partial x} \operatorname{max}(x,y) = 0$ when $(x,y)=(0.1, 0.9)$. So although the composite function $\operatorname{max}(\operatorname{min}(w, x), \operatorname{min}(1-w, 1-x))$ is differentiable and $\btright \neg(x \oplus w)$ it does not always backpropagate error to its inputs. In contrast, $\partial_{\neg}$ always backpropagates error to its inputs because it is a gradient-rich function (see figure \ref{fig:gradient-rich}). + +\begin{definition}[Gradient-rich] + A function, $f: [0,1]^n \rightarrow [0,1]^m$, is {\em gradient-rich} if $\frac{\partial f({\bf x})}{\partial x_{i}} \neq {\bf 0}$ for all ${\bf x} \in \{(x_{1}, \dots, x_{n}) ~|~ x_{i} \in [0,1] \setminus \{1/2\}\}$. +\end{definition} + +$\partial \mathbb{B}$ nets must be composed of `activation' functions that are hard-equivalent to discrete functions but also, where possible, gradient-rich. To meet this requirement we introduce the technique of margin packing. + +\subsection{Margin packing} + +Say we aim to construct a differentiable analogue of $x \wedge y$. Note that $\operatorname{min}(x,y)$ essentially selects one of $x$ or $y$ as a representative soft-bit that is guaranteed hard-equivalent to $x \wedge y$. However, by selecting only one of $x$ or $y$ then $\operatorname{min}$ is also guaranteed to be gradient-sparse. We define a `margin packing' method to solve this dilemma. + +The main idea of margin packing is (i) select a representative bit that is hard-equivalent to the target discrete function, and then (ii) pack a fraction of the margin between the representative bit and the hard threshold $1/2$ with gradient-rich information. The result is an augmented bit that is a function of all inputs yet hard-equivalent to the target function. + +More concretely, say we have a vector of soft-bit inputs ${\bf x}$ and the $i$th element represents the target discrete function (e.g. if our target is $x \wedge y$ then ${\bf x}=[x,y]$ and $i$ is 1 if $x 1/2 \\ +x_{i} + \operatorname{margin-fraction}({\bf x}, i) & \text{otherwise.} +\end{cases} +\end{aligned} +\label{eq:augmented-bit} +\end{equation} +Note that if the representative bit is high (resp. low) then the augmented bit is also high (resp. low). The difference between the augmented and representative bit depends on the size of the available margin and the mean soft-bit value. Almost everywhere, an increase (resp. decrease) of the mean soft-bit increases (resp. decreases) the value of the augmented bit (see figure \ref{fig:margin-trick}). Note that if the $i$th bit is representative (i.e. hard-equivalent to the target function) then so is the augmented bit (see lemma \ref{prop:augmented}). We use margin packing, where appropriate, to define gradient-rich, hard-equivalents of boolean functions. + +\begin{figure}[t!] + \centering + \includegraphics[trim=30pt 5pt 30pt 10pt, clip, width=1.0\textwidth]{margin-trick.png} + \caption{{\em Margin packing for constructing gradient-rich, hard-equivalent functions}. A representative bit, $z$, is hard-equivalent to a discrete target function but gradient-sparse (e.g. $z=\operatorname{min}(x,y) \btright x \wedge y$). On the left $z$ is low, $z<1/2$; on the right $z$ is high, $z>1/2$. We can pack a fraction of the margin between $z$ and the hard threshold $1/2$ with additional gradient-rich information without affecting hard-equivalence. A natural choice is the mean soft-bit, $\bar{\bf x} \in [0,1]$. The grey shaded areas denote the packed margins and the final augmented bit. On the left $\approx 60\%$ of the margin is packed; on the right $\approx 90\%$.} + \label{fig:margin-trick} +\end{figure} +% On the left, ${\bf x}=[0.9,0.23]$, $z=0.23$, $\bar{\bf x}=0.57$ and therefore $\approx 60\%$ of the margin is packed; on the right, ${\bf x}=[0.9,0.83]$, $z=0.83$, $\bar{\bf x}=0.87$, and therefore $\approx 90\%$ of the margin is packed. + +\subsection{Differentiable $\wedge$, $\vee$ and $\Rightarrow$} + +We aim to construct a differentiable analogue of the boolean function $\bigwedge_{i=1}^{n} x_i$. A representative bit is $\operatorname{min}(x_{1},\dots,x_{n})$. The function +\begin{equation*} +\begin{aligned} +\partial_{\wedge}: [0,1]^{n} &\to [0,1], \\ +{\bf x} &\mapsto \operatorname{augmented-bit}({\bf x}, \operatorname{argmin}\limits_{i} x[i]) +\end{aligned} +\end{equation*} +is therefore hard-equivalent to the boolean function $\bigwedge_{i=1}^{n} x_i$ (see proposition \ref{prop:and}). In the special case $n=2$ we get the piecewise function, +\begin{equation*} +\partial_{\wedge}\!(x, y) = + \begin{cases} + 1/2 + 1/2(x + y)(\operatorname{min}(x,y) - 1/2) & \text{if } \operatorname{min}(x,y) > 1/2 \\ + \operatorname{min}(x,y) + 1/2(x + y)(1/2 - \operatorname{min}(x,y)) & \text{otherwise.} + \end{cases} +\end{equation*} +Note that $\partial_{\wedge}$ is differentiable almost everywhere and gradient-rich (see figure \ref{fig:gradient-rich}). + +The differentiable analogue of $\vee$ is identical to $\wedge$, except the representative bit is selected by $\operatorname{max}$. The function +\begin{equation*} +\begin{aligned} +\partial_{\vee}: [0,1]^{n} &\to [0,1], \\ +{\bf x} &\mapsto \operatorname{augmented-bit}({\bf x}, \operatorname{argmax}\limits_{i} x[i]) +\end{aligned} +\end{equation*} +is hard-equivalent to the boolean function $\bigvee_{i=1}^{n} x_i$ (see proposition \ref{prop:or}). Note that $\partial_{\vee}$ is differentiable almost everywhere and gradient-rich (see figure \ref{fig:gradient-rich}). + +\begin{comment} +Define +\begin{equation*} +\begin{aligned} +\partial_{\vee}\!(x, y) = +\begin{cases} +1/2 + 1/2(x + y)(\operatorname{max}(x,y) - 1/2) & \text{if } \operatorname{max}(x,y) > 1/2 \\ +\operatorname{max}(x,y) + 1/2(x + y)(1/2 - \operatorname{max}(x,y)) & \text{otherwise.} +\end{cases} +\end{aligned} +\end{equation*} +\begin{comment} +\begin{equation*} +\begin{aligned} +\partial_{\vee}: [0,1]^{2} &\to [0,1], \\ +(x, y) &\mapsto +\begin{cases} + 1/2 + 1/2(x + y)(m - 1/2) & \text{if } 2m > 1 \\ +m + 1/2(x + y)(1/2 - m) & \text{otherwise,} +\end{cases} +\end{aligned} +\end{equation*} +\end{comment} + +The differentiable analogue of $\Rightarrow$ (material implication) is defined in terms of $\partial_{\vee}$. The function +\begin{equation*} +\begin{aligned} +\partial_{\Rightarrow}: [0,1]^{2} &\to [0,1],\\ +(x, y) &\mapsto \partial_{\vee}\!(y, 1-x)\text{,} +\end{aligned} +\end{equation*} +is hard-equivalent to $x \Rightarrow y$ (see proposition \ref{prop:implies}). We can define analogues of all the basic boolean operators in a similar manner. + +\subsection{Differentiable majority} + +\begin{figure}[t] + \centering + \includegraphics[trim=0pt 0pt 0pt 0pt, clip, width=1.0\textwidth]{majority-gates.png} + \caption{{\em Differentiable boolean majority.} The boolean majority function for three variables in DNF form is $\operatorname{Maj}(x,y,z) = (x \wedge y) \vee (x \wedge y) \vee (y \wedge z)$. The upper row contains contour plots of $f(x,y,z) = \operatorname{min}(\operatorname{max}(x,y), \operatorname{max}(x,z), \operatorname{max}(y,z))$ for values of $z \in \{0.2, 0.4, 0.6, 0.8\}$. $f$ is differentiable and $\btright\!\operatorname{Maj}$ but gradient-sparse (vertical and horizontal contours indicate constancy with respect to an input). Also, the number of terms in $f$ grows exponentially with the number of variables. The lower row contains contour plots of $\partial\!\operatorname{Maj}(x,y,z)$ for the same values of $z$. $\partial\!\operatorname{Maj}$ is differentiable and $\btright\!\operatorname{Maj}$ yet gradient-rich (curved contours indicate variability with respect to any inputs). In addition, the number of terms in $\partial\!\operatorname{Maj}$ is constant with respect to the number of variables.} + \label{fig:majority-plot} +\end{figure} + +The boolean majority function is particularly important for tractable learning because it is a threshold function: +\begin{equation*} +\begin{aligned} +\operatorname{Maj}: \{0,1\}^{n} &\to \{0,1\},\\ +{\bf x} &\mapsto \left\lfloor +\frac{1}{2} + \frac{\sum_{i=1}^{n} x_{i} - 1/2}{n} +\right\rfloor\text{,} +\end{aligned} +\end{equation*} +where we count $\operatorname{False}$ as $0$ and $\operatorname{True}$ as $1$. Interpret each input bit $x_{i}$ as a vote, yes or no, for a binary decision. If the majority of voters are in favour then $\operatorname{Maj}$ outputs 1. The majority function, in the context of a predictive model, aggregates multiple bits of weak evidence into a hard decision.We aim to construct a differentiable analogue of $\operatorname{Maj}$. + +$\operatorname{Maj}$ for $n$ bits in DNF form is a disjunction of $\binom{n}{k}$ conjunctive clauses of size $k$, where $k=\lceil n/2 \rceil$. Each clause checks whether a unique combination of a majority of the $n$ bits are all high, e.g. $\operatorname{Maj}(x, y, z) = (x \wedge y) \vee (x \wedge y) \vee (y \wedge z)$. In principle we can implement a differentiable analogue of $\operatorname{Maj}$ in terms of $\partial_{\wedge}$ and $\partial_{\vee}$. However, the number of terms grows exponentially with the variables (e.g. $n=50$ generates over 100 trillion clauses, which is infeasible). And no general algorithm exists to find the minimal representation of $\operatorname{Maj}$ for arbitrary $n$. + +Instead, we trade-off time for memory costs. Observe that if the function $\operatorname{sort}({\bf x})$ sorts the elements of ${\bf x}$ in ascending order then the `median' soft-bit is representative. For example, if ${\bf x} = [0.4, 0.9, 0.2]$ then $\operatorname{sort}({\bf x}) = [0.2, 0.4, 0.9]$ and the `median' bit $x_{2}=0.4$ is low, which is hard-equivalent to $\operatorname{Maj}(0, 1, 0) = 0$. Define the index of the `median' bit by +\begin{equation*} +\begin{aligned} +\operatorname{majority-index}: [0, 1]^{n} & \to \mathbb{Z}_{> 0}\\ +{\bf x} & \mapsto \left\lceil \frac{|{\bf x}|}{2} \right\rceil +\text{.} +\end{aligned} +\end{equation*} +Then, applying margin packing, define the differentiable function +\begin{equation*} +\begin{aligned} + \partial\!\operatorname{Maj}: [0,1]^{n} &\to [0,1], \\ + {\bf x} &\mapsto \operatorname{augmented-bit}(\operatorname{sort}({\bf x}), \operatorname{majority-index}({\bf x}))\text{,} +\end{aligned} +\end{equation*} +which is hard-equivalent to $\operatorname{Maj}$ (see theorem \ref{prop:majority}). Note that $\partial\!\operatorname{Maj}$ is differentiable almost everywhere and gradient-rich (see figure \ref{fig:majority-plot}). If $\operatorname{sort}$ is quicksort then the the average time-complexity of $\partial\!\operatorname{Maj}$ is $\mathcal{O}(n\log{}n)$, which makes $\partial\!\operatorname{Maj}$ more expensive than $\partial_{\neg}$, $\partial_{\wedge}$, $\partial_{\vee}$ and $\partial_{\Rightarrow}$ at training time. However, in the hard $\partial\mathbb{B}$ net we efficiently implement $\operatorname{Maj}$ as a discrete program that simply checks if the majority of bits are high. Note that we use sorting to define a differentiable function that is exactly equivalent to a discrete function (rather than defining a continuous approximation to sorting, e.g. \cite{NEURIPS2019_d8c24ca8}). + +\subsection{Differentiable counting} + +A boolean counting function $f({\bf x})$ is $\operatorname{True}$ if a counting predicate, $c({\bf x})$, holds over its $n$ inputs. We aim to construct a differentiable analogue of $\operatorname{count}({\bf x}, k)$ where $c({\bf x}) := |\{x_{i} : x_{i} = 1 \}| = k$ (i.e. `exactly $k$ high'), which can be useful in multiclass classification problems. + +As before, we use $\operatorname{sort}$ to trade-off time for memory costs. Observe that if the elements of ${\bf x}$ are in ascending order then, if any soft-bits are high, there exists a unique contiguous pair of indices $(i,i+1)$ where $x_{i}$ is low and $x_{i+1}$ is high, where index $i$ is a direct count of the number of soft-bits that are low in ${\bf x}$. In consequence, define +\begin{equation*} +\begin{aligned} +\partial\!\operatorname{count-hot}: [0,1]^{n} &\to [0,1]^{n+1}, \\ +{\bf x} &\mapsto \operatorname{low-high}(\operatorname{sort}({\bf x}))\text{,} +\end{aligned} +\end{equation*} +where +\begin{equation*} +\begin{aligned} +\operatorname{low-high}: [0,1]^{n} &\to [0,1]^{n+1},\\ +{\bf x} &\mapsto \left[ \partial_{\wedge}\!(1, x_{1}), \partial_{\wedge}\!(1 - x_{1}, x_{2}), \dots, \partial_{\wedge}\!(1 - x_{n-1}, x_{n}), \partial_{\wedge}\!(1-x_{n}, 1) \right]\text{.} +\end{aligned} +\end{equation*} +$\partial\!\operatorname{count-hot}({\bf x})$ outputs a 1-hot vector where the index of high bit is the number of low bits in ${\bf x}$. For example, $\partial\!\operatorname{count-hot}([0.1, 0.9, 0.2]) = [0.1, 0.2, \bold{0.8}, 0.1]\text{,}$ indicating that 2 bits are low, and $\partial\!\operatorname{count-hot}([0.6, 0.9, 0.7]) = [\bold{0.6}, 0.4, 0.3, 0.1]\text{,}$ indicating that 0 bits are low. Note that $\partial\!\operatorname{count-hot}$ is differentiable, gradient-rich and hard-equivalent to the boolean function +\begin{equation*} +\begin{aligned} +\operatorname{count-hot}: \{0,1\}^{n} &\to \{0,1\}^{n+1}, \\ +{\bf x} &\mapsto \left[\operatorname{k-of-n}({\bf x}, 0), \operatorname{k-of-n}({\bf x}, 1), \dots, \operatorname{k-of-n}({\bf x}, n)\right]\text{,} +\end{aligned} +\end{equation*} +where +\begin{equation*} +\operatorname{k-of-n}({\bf x}, k) = \bigvee_{|S|=k} \bigwedge_{i\in S} x_i \bigwedge_{j\notin S} \neg x_j +\end{equation*} +(see proposition \ref{prop:count}). However, in the hard $\partial\mathbb{B}$ net we efficiently implement $\operatorname{count-hot}$ as a discrete program that simply counts the number of low bits. + +We can construct various kinds of boolean counting functions from $\partial\!\operatorname{count-hot}$. For example, $\partial\!\operatorname{count}({\bf x}, k)$ is straightforwardly $\partial\!\operatorname{count-hot}({\bf x})[k]$ where we can use margin-packing to ensure that this single soft-bit is gradient-rich. + +This basic set of boolean functions is sufficient to learn non-trivial relationships from data. We now turn to constructing $\partial\mathbb{B}$ nets from compositions of these functions. + +\subsection{Boolean logic layers} + +The fully variety of $\partial\mathbb{B}$ net architectures is to be explored. Here we focus on defining basic layers sufficient for the classification experiments in section \ref{sec:experiments}. Other kinds of layers, such as convolutional, or real encoders/decoders for regression problems, will be addressed in a sequel. + +A $\partial_{\neg} \!\operatorname{Layer}$ of width $n$ learns to negate up to $n$ different subsets of the elements of its input vector: +\begin{equation*} +\begin{aligned} +\partial_{\neg} \!\operatorname{Layer}: [0,1]^{n \times m} \times [0,1]^{m} &\to [0,1]^{n \times m}, \\ +({\bf W}, {\bf x}) &\mapsto +\begin{bmatrix} +\partial_{\neg}(w_{1,1}, x_{1}) & \dots & \partial_{\neg}(w_{1,m}, x_{m}) \\ +\vdots & \ddots & \vdots \\ +\partial_{\neg}(w_{n,1}, x_{1}) & \dots & \partial_{\neg}(w_{n,m}, x_{m}) +\end{bmatrix} +\end{aligned} +\end{equation*} +where ${\bf x}$ is a soft-bit input vector, ${\bf W}$ is a weight matrix and $n$ is the layer width. Similarly, A $\partial_{\Rightarrow} \!\operatorname{Layer}$ of width $n$ learns to `mask to true or $\operatorname{nop}$' up to $n$ different subsets of the elements of its input vector: +\begin{equation*} +\partial_{\Rightarrow} \!\operatorname{Layer}({\bf W}, {\bf x}) = +\begin{bmatrix} +\partial_{\Rightarrow}(w_{1,1}, x_{1}) & \dots & \partial_{\Rightarrow}(w_{1,m}, x_{m}) \\ +\vdots & \ddots & \vdots \\ +\partial_{\Rightarrow}(w_{n,1}, x_{1}) & \dots & \partial_{\Rightarrow}(w_{n,m}, x_{m}) +\end{bmatrix}\text{.} +\end{equation*} +A $\partial_{\wedge}\!\operatorname{Neuron}$ learns to logically $\wedge$ a subset of its input vector: +\begin{equation*} +\begin{aligned} +\partial_{\wedge}\!\operatorname{Neuron}: [0,1]^{n} \times [0,1]^{n} &\to [0,1], \\ +({\bf w}, {\bf x}) &\mapsto \min(\partial_{\Rightarrow}\!(w_{1}, x_{1}), \dots, \partial_{\Rightarrow}\!(w_{n}, x_{n}))\text{,} +\end{aligned} +\end{equation*} +where ${\bf w}$ is a weight vector. Each $\partial_{\Rightarrow}(w_{i},x_{i})$ learns to include or exclude $x_{i}$ from the conjunction depending on weight $w_{i}$. For example, if $w_{i}>0.5$ then $x_{i}$ affects the value of the conjunction since $\partial_{\Rightarrow}(w_{i},x_{i})$ passes-through a soft-bit that is high if $x_{i}$ is high, and low otherwise; but if $w_{i} \leq 0.5$ then $x_{i}$ does not affect the conjunction since $\partial_{\Rightarrow}(w_{i},x_{i})$ always passes-through a high soft-bit. A $\partial_{\wedge}\!\operatorname{Layer}$ of width $n$ learns up to $n$ different conjunctions of subsets of its input (of whatever size). A $\partial_{\vee}\!\operatorname{Neuron}$ is defined similarly: +\begin{equation*} +\begin{aligned} +\partial_{\vee}\!\operatorname{Neuron}: [0,1]^{n} \times [0,1]^{n} &\to [0,1], \\ +({\bf w}, {\bf x}) &\mapsto \max(\partial_{\wedge}\!(w_{1}, x_{1}), \dots, \partial_{\wedge}\!(w_{n}, x_{n}))\text{.} +\end{aligned} +\end{equation*} +Each $\partial_{\wedge}(w_{i},x_{i})$ learns to include or exclude $x_{i}$ from the disjunction depending on weight $w_{i}$. A $\partial_{\vee}\!\operatorname{Layer}$ of width $n$ learns up to $n$ different disjunctions of subsets of its input (of whatever size). +%For example, if $w_{i}>0.5$ then $x_{i}$ affects the value of the conjunction because $\partial_{\wedge}(w_{i},x_{i})$ passes-through a soft-bit that is high if $x_{i}$ is high, and low otherwise; but if $w_{i} \leq 0.5$ then $x_{i}$ does not affect the conjunction because $\partial_{\Rightarrow}(w_{i},x_{i})$ always passes-through a low soft-bit. + +We can compose $\partial_{\neg}$, $\partial_{\wedge}$ and $\partial_{\vee}$ layers to learn boolean formulae of arbitrary width and depth. + +\subsection{Classification layers} + +In classification problems the final layer of a neural network is typically interpreted as a vector of real-valued logits, one for each label, where the index of the maximum logit indicates the most probable label. However, we cannot interpret a soft-bit vector as logits without violating hard-equivalence. In addition, when training $\partial\mathbb{B}$ nets, loss functions should be a function of hardened bits, otherwise gradient descent may non-optimally traverse trajectories that take no account of the hard threshold at $1/2$. For example, consider that an instance is correctly classified by a 1-hot vector with high bit $x=0.51$. Updating the net's weights to change this value to $0.51+\epsilon$ will not improve accuracy and may prevent the correct classification of a different instance. + +For these reasons, $\partial\mathbb{B}$ nets have a final `hardening' layer to ensure that loss is a function of hard, not soft, bits: +\begin{equation*} +\begin{aligned} +\partial\!\operatorname{harden}: [0,1]^{n} &\to [0,1]^{n}, \\ +{\bf x} &\mapsto \operatorname{harden}({\bf x})\text{.} +\end{aligned} +\end{equation*} +The $\operatorname{harden}$ function is not differentiable and therefore $\partial\!\operatorname{harden}$ uses the straight-through estimator \citep{DBLP:journals/corr/BengioLC13} during backpropagation. By restricting the use of the straight-through estimator to final layers we avoid compounding gradient estimation errors to deeper parts of the network. Note that $\partial\!\operatorname{harden}$ is hard-equivalent to a $\operatorname{nop}$. + +$\partial\mathbb{B}$ nets can re-use many of the techniques deployed in standard neural networks. For example, for improved generalisation, we define a `boolean' analogue of the dropout layer \citep{JMLR:v15:srivastava14a}: +\begin{equation*} +\begin{aligned} +\partial\!\operatorname{dropout}: [0,1]^{n} \times [0,1] &\to [0,1]^{n}, \\ +({\bf x}, p) &\mapsto [f(x_{1}, p), \dots, f(x_{n}, p)]\text{,} +\end{aligned} +\end{equation*} +where +\begin{equation*} +f(x, p) = \begin{cases} +1 - x, & \text{with probability } p \\ +x, & \text{otherwise.} +\end{cases} +\end{equation*} +At train time $\partial\!\operatorname{dropout}$ randomly negates soft-bit values with probability $p$. At test time, and in the hard-net, $\partial\!\operatorname{dropout}$ is a $\operatorname{nop}$. + +\begin{figure}[t!] + \centering + \includegraphics[width=0.6\textwidth]{toy-example-architecture.png} + \caption{{\em A $\partial\mathbb{B}$ net to illustrate hardening}. The net concatenates a $\partial_{\neg}\!\operatorname{Layer}$ (of width $n$) with a reshaping layer that outputs two vectors, which get reduced, by a $\partial\!\operatorname{Maj}$ operator, to 2 soft-bits, one for each class label. A final $\partial\!\operatorname{harden}$ layer ensures the loss is a function of hard bits. When $|{\bf x}|=1$ we choose $n=2$ and therefore the net's weights, once hardened, consume $2$ bits. When $|{\bf x}|=5$ we choose $n=8$ and the weights consume $40$ bits ($5$ bytes).} + \label{fig:toy-example-architecture} +\end{figure} + +\section{Experiments}\label{sec:experiments} + +The $\partial\mathbb{B}$ net library is implemented in Flax \citep{flax2020github} and JAX \citep{jax2018github} and available at {\small \url{github.com/Z80coder/db-nets}}. The library supports the specification of a $\partial\mathbb{B}$ net as Python code, which automatically defines (i) the soft-net for training (weights are floats), (ii) a hard-net for inference (weights are booleans), and (iii) a symbolic net for interpretation (weights and inputs are symbols). The symbolic net, when evaluated, interprets its own JAX expression and outputs a description of the discrete program it computes. + +We compare the performance of $\partial\mathbb{B}$ nets against standard ML approaches on three problems: the classic Iris dataset, an adversarial noisy XOR problem, and MNIST. But first we illustrate the kind of discrete program that a $\partial\mathbb{B}$ net learns. + +\subsection{Hardening} + +We present a toy problem to illustrate hard-equivalence. Consider the trivial problem of predicting whether a person wears a $\operatorname{t-shirt}$ (label 0) or a $\operatorname{coat}$ (label 1) conditional on the single feature $\operatorname{outside}$ (0 = False, and 1 = True). The training and test data consist of the examples in table \ref{tab:toy1}. + +\begin{table}[h!] + \centering + \begin{tabular}{|c|c|} + $\operatorname{outside}$ & $\operatorname{label}$ \\ \hline + 0 & 0 \\ + 1 & 1 + \end{tabular} + \caption{A trivial learning problem} + \label{tab:toy1} +\end{table} + +We use the $\partial\mathbb{B}$ net described in figure \ref{fig:toy-example-architecture}, which is hard-equivalent to the discrete program: + +\begin{lstlisting}[language=Python,style=mystyle,frame=single] +def dbNet(outside): + return [ + ge(sum((0, not(xor(ne(outside, 0), w1)))), 1), + ge(sum((0, not(xor(ne(outside, 0), w2)))), 1) + ] +\end{lstlisting} + +with trainable weights $w_{1}$ and $w_{2}$. We randomly initialize the network and train using the RAdam optimizer \citep{Liu2020On} with softmax cross-entropy loss until training and test accuracies are both $100\%$. We harden the learned weights to get $w_{1} = \operatorname{False}$ and $w_{2} = \operatorname{True}$, and bind with the discrete program, which then symbolically simplifies to: + +\begin{lstlisting}[language=Python,style=mystyle,frame=single] +def dbNet(outside): + return [not(outside), outside] +\end{lstlisting} + +which is directly interpretable as `when outside wear a $\operatorname{coat}$, otherwise wear a $\operatorname{t-shirt}$'. + +Hardening scales to arbitrarily complex $\partial\mathbb{B}$ nets. Interpreting the net's predictions requires automatic symbolic simplification. For example, introduce 4 additional boolean features: $\operatorname{very-cold}$, $\operatorname{cold}$, $\operatorname{warm}$, and $\operatorname{very-warm}$. The training and test data consists of examples like those in table \ref{tab:toy2}. + +\begin{table}[h!] + \centering + \begin{tabular}{|c|c|c|c|c|c|} + $\operatorname{very-cold}$ & $\operatorname{cold}$ & $\operatorname{warm}$ & $\operatorname{very-warm}$ & $\operatorname{outside}$ & $\operatorname{label}$ \\ \hline + 1 & 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 \\ + \dots & \dots & \dots & \dots & \dots & \dots + \end{tabular} + \caption{A toy learning problem} + \label{tab:toy2} +\end{table} + +We use the same architecture but increase the width of the $\partial_{\neg}\!\operatorname{Layer}$ from 2 to 8. The net is now hard-equivalent to the discrete program: + +\begin{comment} +\begin{lstlisting}[language=Python,style=mystyle,frame=single] +def dbNet(very-cold, cold, warm, very-warm, outside): + return [ + ge(sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((0, not(xor(ne(very-cold, 0), False)))), not(xor(ne(cold, 0), True)))), not(xor(ne(warm, 0), True)))), not(xor(ne(very-warm, 0), True)))), not(xor(ne(outside, 0), True)))), not(xor(ne(very-cold, 0), True)))), not(xor(ne(cold, 0), False)))), not(xor(ne(warm, 0), False)))), not(xor(ne(very-warm, 0), True)))), not(xor(ne(outside, 0), False)))), not(xor(ne(very-cold, 0), False)))), not(xor(ne(cold, 0), False)))), not(xor(ne(warm, 0), True)))), not(xor(ne(very-warm, 0), False)))), not(xor(ne(outside, 0), False)))), not(xor(ne(very-cold, 0), False)))), not(xor(ne(cold, 0), False)))), not(xor(ne(warm, 0), True)))), not(xor(ne(very-warm, 0), False)))), not(xor(ne(outside, 0), False)))), 11), + ge(sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((0, not(xor(ne(very-cold, 0), True)))), not(xor(ne(cold, 0), False)))), not(xor(ne(warm, 0), False)))), not(xor(ne(very-warm, 0), False)))), not(xor(ne(outside, 0), False)))), not(xor(ne(very-cold, 0), True)))), not(xor(ne(cold, 0), True)))), not(xor(ne(warm, 0), False)))), not(xor(ne(very-warm, 0), True)))), not(xor(ne(outside, 0), True)))), not(xor(ne(very-cold, 0), False)))), not(xor(ne(cold, 0), True)))), not(xor(ne(warm, 0), False)))), not(xor(ne(very-warm, 0), True)))), not(xor(ne(outside, 0), False)))), not(xor(ne(very-cold, 0), False)))), not(xor(ne(cold, 0), True)))), not(xor(ne(warm, 0), False)))), not(xor(ne(very-warm, 0), False)))), not(xor(ne(outside, 0), True)))), 11)] +\end{lstlisting} +\end{comment} + +\begin{lstlisting}[language=Python,style=mystyle,frame=single] +def dbNet(very-cold, cold, warm, very-warm, outside): + return [ + ge(sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((0, not(xor(ne(very-cold, 0), w1)))), not(xor(ne(cold, 0), w2)))), not(xor(ne(warm, 0), w3)))), not(xor(ne(very-warm, 0), w4)))), not(xor(ne(outside, 0), w5)))), not(xor(ne(very-cold, 0), w6)))), not(xor(ne(cold, 0), w7)))), not(xor(ne(warm, 0), w8)))), not(xor(ne(very-warm, 0), w9)))), not(xor(ne(outside, 0), w10)))), not(xor(ne(very-cold, 0), w11)))), not(xor(ne(cold, 0), w12)))), not(xor(ne(warm, 0), w13)))), not(xor(ne(very-warm, 0), w14)))), not(xor(ne(outside, 0), w15)))), not(xor(ne(very-cold, 0), w16)))), not(xor(ne(cold, 0), w17)))), not(xor(ne(warm, 0), w18)))), not(xor(ne(very-warm, 0), w19)))), not(xor(ne(outside, 0), w20)))), 11), + ge(sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((sum((0, not(xor(ne(very-cold, 0), w21)))), not(xor(ne(cold, 0), w22)))), not(xor(ne(warm, 0), w23)))), not(xor(ne(very-warm, 0), w24)))), not(xor(ne(outside, 0), w25)))), not(xor(ne(very-cold, 0), w26)))), not(xor(ne(cold, 0), w27)))), not(xor(ne(warm, 0), w28)))), not(xor(ne(very-warm, 0), w29)))), not(xor(ne(outside, 0), w30)))), not(xor(ne(very-cold, 0), w31)))), not(xor(ne(cold, 0), w32)))), not(xor(ne(warm, 0), w33)))), not(xor(ne(very-warm, 0), w34)))), not(xor(ne(outside, 0), w35)))), not(xor(ne(very-cold, 0), w36)))), not(xor(ne(cold, 0), w37)))), not(xor(ne(warm, 0), w38)))), not(xor(ne(very-warm, 0), w39)))), not(xor(ne(outside, 0), w40)))), 11) + ] +\end{lstlisting} +We train the $[w_{1}, \dots, w_{40}]$ soft-bit weights as before then harden to 40 boolean weights and bind with the discrete program. Post-training the program symbolically simplifies to: + +\begin{lstlisting}[language=Python,style=mystyle,frame=single] +def dbNet(very-cold, cold, warm, very-warm, outside): + return [ + 4 !very-cold + 4 !cold + (3 warm + !warm) + (very-warm + 3 !very-warm) + (outside + 3 !outside) >= 11, + (very-cold + 3 !very-cold) + 4 cold + 4 !warm + (3 very-warm + !very-warm) + 2 (outside + !outside) >= 11 + ] +\end{lstlisting} + +The predictions linearly weight multiple pieces of evidence due to the presence of the $\partial\!\operatorname{Maj}$ operator (which is probably overkill for this toy problem). From this expression we can read-off that the $\partial\mathbb{B}$ net has learned `if not $\operatorname{very-cold}$ and not $\operatorname{cold}$ and not $\operatorname{outside}$ then wear a $\operatorname{t-shirt}$'; and `if $\operatorname{cold}$ and not ($\operatorname{warm}$ or $\operatorname{very-warm}$) and $\operatorname{outside}$ then wear a $\operatorname{coat}$' etc. The discrete program is more interpretable compared to typical neural networks, and can be exactly encoded as a SAT problem in order to verify its properties, such as robustness. + +\begin{figure}[t!] + \centering + \includegraphics[width=0.8\textwidth]{binary-iris-architecture.png} + \caption{{\em A $\partial\mathbb{B}$ net for the binary Iris problem}. The net concatenates the soft-bit input, ${\bf x}$ (length 16), with its negation, ${\bf 1 - x}$, and supplies the resulting vector (length 32) to a $\partial_{\wedge}\!\operatorname{Layer}$ (width 59), a $\partial\!\operatorname{dropout}$ layer for improved generalisation, a $\partial\!\operatorname{count-hot}$ layer that generates a 1-hot vector (width 60) that is reduced by $\operatorname{max}$ to a 1-hot vector of 3 classification bits. A final $\partial\!\operatorname{harden}$ ensures the loss is a function of hard bits. The net's weights, once hardened, consume $236$ bytes.} + \label{fig:binary-iris-architecture} +\end{figure} + +\subsection{Binary Iris} + +The Iris dataset has 150 examples with 4 inputs (sepal length and width, and petal length and width), and 3 labels ({\em setosa}, {\em versicolour}, and {\em virginica}). We use the binary version of the Iris dataset \citep{binary-iris-dataset} where each input float is represented by 4 bits. We perform 1000 experiments, each with a different random seed. Each experiment randomly partitions the data into 80\% training and 20\% test sets. We initialize the network, described in figure \ref{fig:binary-iris-architecture}, with all weights $w_{i} = 0.3$ and train for 1000 epochs with the RAdam optimizer and softmax cross-entropy loss. + +We measure the accuracy of the final net to avoid hand-picking the best configuration. Table \ref{tab:binary-iris-results} compares the $\delta\mathbb{B}$ net against other classifiers \citep{granmo18}. Naive Bayes performs the worst. The Tsetlin machine performs best on this problem, with the $\partial\mathbb{B}$ net second. + +\begin{table}[t] + \centering + \begin{tabular}{llllll} + \cline{2-6} + \multicolumn{1}{c}{} & \multicolumn{5}{c}{\textbf{accuracy}} \\ \cline{2-6} + \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{mean} & \multicolumn{1}{l|}{5 \%ile} & \multicolumn{1}{l|}{95 \%ile} & \multicolumn{1}{l|}{min} & \multicolumn{1}{l|}{max} \\ \hline + \multicolumn{1}{|l|}{Tsetlin} & \multicolumn{1}{l|}{95.0 +/- 0.2} & \multicolumn{1}{l|}{86.7} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{80.0} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{$\partial\mathbb{B}$} & \multicolumn{1}{l|}{\textbf{93.9 +/- 0.1}} & \multicolumn{1}{l|}{\textbf{86.7}} & \multicolumn{1}{l|}{\textbf{100.0}} & \multicolumn{1}{l|}{\textbf{80.0}} & \multicolumn{1}{l|}{\textbf{100.0}} \\ \hline + \multicolumn{1}{|l|}{neural network} & \multicolumn{1}{l|}{93.8 +/- 0.2} & \multicolumn{1}{l|}{86.7} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{80.0} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{SVM} & \multicolumn{1}{l|}{93.6 +/- 0.3} & \multicolumn{1}{l|}{86.7} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{76.7} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{naive Bayes} & \multicolumn{1}{l|}{91.6 +/- 0.3} & \multicolumn{1}{l|}{83.3} & \multicolumn{1}{l|}{96.7} & \multicolumn{1}{l|}{70.0} & \multicolumn{1}{l|}{100.0} \\ \hline + \end{tabular} + \caption{{\em Ranked binary Iris results} measured over 1000 experiments.} + \label{tab:binary-iris-results} +\end{table} + +\begin{figure}[t!] + \centering + \includegraphics[width=0.8\textwidth]{noisy-xor-architecture.png} + \caption{{\em A $\partial\mathbb{B}$ net for the noisy xor problem}. The net concatenates the soft-bit input, ${\bf x}$ (length 12), with its negation, ${\bf 1 - x}$, and supplies the resulting vector (length 24) to a $\partial_{\wedge}\!\!\operatorname{Layer}$ (width 32), $\partial_{\vee}\!\!\operatorname{Layer}$ (width 32), $\partial_{\neg} \!\operatorname{Layer}$ (width 16), and a final $\partial\!\operatorname{Maj}$ to produce a single soft-bit $y \in [0,1]$ (to predict odd parity) and its negation $1-y$ (to predict even parity). The net's weights, once hardened, consume $288$ bytes.} + \label{fig:noisy-xor-architecture} +\end{figure} + +\subsection{Noisy XOR} + +The noisy XOR dataset \citep{noisy-xor-dataset} is an adversarial parity problem with noisy non-informative features. The dataset consists of 10K examples with 12 boolean inputs and a target label (where 0 = odd and 1 = even) that is a XOR function of 2 of the inputs. The remaining 10 inputs are entirely random. We train on 50\% of the data where, additionally, 40\% of the labels are inverted. We initialize the network described in figure \ref{fig:noisy-xor-architecture} with random weights distributed close to the hard threshold at $1/2$ (i.e. in the $\partial_{\wedge}\!\operatorname{Layer}$, $w_{i} = 0.501 \times b + 0.3 \times (1-b)$ where $b \sim \operatorname{Bernoulli}(0.01)$; in the $\partial_{\vee}\!\operatorname{Layer}$, $w_{i} = 0.7 \times b + 0.499 \times (1-b)$ where $b \sim \operatorname{Bernoulli}(0.99)$); and in the $\partial_{\neg}\!\operatorname{Layer}$, $w_{i} \sim \operatorname{Uniform}(0.499, 0.501)$. We train for 2000 epochs with the RAdam optimizer and softmax cross-entropy loss. + +We measure the accuracy of the final net on the test data to avoid hand-picking the best configuration. Table \ref{tab:noisy-xor-results} compares the $\partial\mathbb{B}$ net against other classifiers \citep{granmo18}. The high noise causes logistic regression and naive Bayes to randomly guess. The SVM hardly performs better. In constrast, the multilayer neural network, Tsetlin machine, and $\partial\mathbb{B}$ net all successfully learn the underlying XOR signal. The Tsetlin machine performs best on this problem, with the $\partial\mathbb{B}$ net second. + +\begin{table}[t] + \centering + \begin{tabular}{llllll} + \cline{2-6} + \multicolumn{1}{c}{} & \multicolumn{5}{c}{\textbf{accuracy}} \\ \cline{2-6} + \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{mean} & \multicolumn{1}{l|}{5 \%ile} & \multicolumn{1}{l|}{95 \%ile} & \multicolumn{1}{l|}{min} & \multicolumn{1}{l|}{max} \\ \hline + \multicolumn{1}{|l|}{Tsetlin} & \multicolumn{1}{l|}{99.3 +/- 0.3} & \multicolumn{1}{l|}{95.9} & \multicolumn{1}{l|}{100.0} & \multicolumn{1}{l|}{91.6} & \multicolumn{1}{l|}{100.0} \\ \hline + \multicolumn{1}{|l|}{$\partial\mathbb{B}$} & \multicolumn{1}{l|}{\textbf{97.9 +/- 0.2}} & \multicolumn{1}{l|}{\textbf{95.4}} & \multicolumn{1}{l|}{\textbf{100.0}} & \multicolumn{1}{l|}{\textbf{93.6}} & \multicolumn{1}{l|}{\textbf{100.0}} \\ \hline + \multicolumn{1}{|l|}{neural network} & \multicolumn{1}{l|}{95.4 +/- 0.5} & \multicolumn{1}{l|}{90.1} & \multicolumn{1}{l|}{98.6} & \multicolumn{1}{l|}{88.2} & \multicolumn{1}{l|}{99.9} \\ \hline + \multicolumn{1}{|l|}{SVM} & \multicolumn{1}{l|}{58.0 +/- 0.3} & \multicolumn{1}{l|}{56.4} & \multicolumn{1}{l|}{59.2} & \multicolumn{1}{l|}{55.4} & \multicolumn{1}{l|}{66.5} \\ \hline + \multicolumn{1}{|l|}{naive Bayes} & \multicolumn{1}{l|}{49.8 +/- 0.2} & \multicolumn{1}{l|}{48.3} & \multicolumn{1}{l|}{51.0} & \multicolumn{1}{l|}{41.3} & \multicolumn{1}{l|}{52.7} \\ \hline + \multicolumn{1}{|l|}{logistic regression} & \multicolumn{1}{l|}{49.8 +/- 0.3} & \multicolumn{1}{l|}{47.8} & \multicolumn{1}{l|}{51.1} & \multicolumn{1}{l|}{41.1} & \multicolumn{1}{l|}{53.1} \\ \hline + \end{tabular} + \caption{{\em Ranked noisy XOR results} measured over 100 experiments.} + \label{tab:noisy-xor-results} +\end{table} + +\begin{figure}[t!] + \centering + \includegraphics[width=0.7\textwidth]{mnist-architecture.png} + \caption{{\em A non-convolutional $\partial\mathbb{B}$ net for MNIST}. The input is a $28\times28$ bit matrix representing an image. The net consists of a $\partial_{\Rightarrow}\!\operatorname{Layer}$ (of width 60, to produce a $2940\times16$ reshaped array), a $\partial\!\operatorname{Maj}$ layer (to produce a vector of size $2940$), a $\partial_{\neg}\!\operatorname{Layer}$ (of width 20, to produce a $20 \times 2940$ array), and a final $\partial\!\operatorname{harden}$ operator to generate hard-bits split into 10 buckets and summed to produce 10 integer logits. The net's weights, once hardened, consume 13.23 kb.} + \label{fig:mnist-architecture} +\end{figure} + +\subsection{MNIST} + +\begin{table}[t] + \centering + \begin{tabular}{lc} + \cline{2-2} + & \textbf{accuracy} \\ \hline + \multicolumn{1}{|l|}{\em 2-layer NN, 800 HU, cross-entropy loss} & \multicolumn{1}{c|}{98.6} \\ \hline + \multicolumn{1}{|l|}{Tsetlin} & \multicolumn{1}{c|}{98.2 +/- 0.0} \\ \hline + \multicolumn{1}{|l|}{\em K-nearest-neighbours, L3} & \multicolumn{1}{c|}{97.2} \\ \hline + \multicolumn{1}{|l|}{$\partial\mathbb{B}$} & \multicolumn{1}{c|}{\textbf{94.0}} \\ \hline + \multicolumn{1}{|l|}{Logistic regression} & \multicolumn{1}{c|}{91.5} \\ \hline + \multicolumn{1}{|l|}{\em Linear classifier (1-layer NN)} & \multicolumn{1}{c|}{88.0} \\ \hline + \multicolumn{1}{|l|}{Decision tree} & \multicolumn{1}{c|}{87.8} \\ \hline + \multicolumn{1}{|l|}{Multinomial Naive Bayes} & \multicolumn{1}{c|}{83.2} \\ \hline + \end{tabular} + \caption{{\em Ranked MNIST results}. A classifier in {\em italics} was trained on grey-value pixel data, otherwise the classifier was trained on binarized data. Note: the $\partial\mathbb{B}$ results are from a small model that under-fits the data (due to OOM errors on my GPU). The next draft will include results using a larger $\partial\mathbb{B}$ net.} + \label{tab:mnist-table} +\end{table} + +The MNIST dataset \citep{726791} consists of 60K training and 10K test examples of handwritten digits (0-9). We binarize the data by replacing pixels with grey value greater than 0.3 with 1, otherwise with 0. We initialize the network described in figure \ref{fig:mnist-architecture} with random weights distributed as $w_{i} = 0.501 \times b + 0.3 \times (1-b)$ where $b \sim \operatorname{Bernoulli}(0.01)$. We train for 1000 epochs with a batch size of 6000 using the RAdam optimizer and softmax cross-entropy loss. + +We measure the accuracy on the final net. Table \ref{tab:mnist-table} compares the $\partial\mathbb{B}$ net against other classifiers (reference data taken from \cite{granmo18} and \url{yann.lecun.com/exdb/mnist}). Basic versions of the algorithms (e.g. no convolutional nets) are applied to unenhanced data (e.g. no data augmentation). The aim is to compare raw performance rather than optimise for MNIST. A 2-layer neural network trained on grey-value pixel data performs best. A Tsetlin machine of 40,000 automata each with 256 states (and therefore 40 kb of parameters) trained on binary data achieves $\approx 98.2\%$ accuracy. A $\partial\mathbb{B}$ net with 105,840 soft-bit weights that harden to 1-bit booleans (and therefore 13.23 kb of parameters) trained on binary data achieves $\approx 94.0\%$ accuracy. However, this $\partial\mathbb{B}$ net underfits the training data and we expect better performance from a larger model. + +\section{Conclusion}\label{sec:conclusion} + +$\partial\mathbb{B}$ nets are differentiable neural networks that are hard-equivalent to non-differentiable, boolean-valued functions. $\partial\mathbb{B}$ nets can therefore learn discrete functions by gradient descent. The main novelty of $\partial\mathbb{B}$ nets is the semantic equivalence between their two aspects: a differentiable soft-net and a non-differentiable hard-net. Maintaining this semantic equivalence requires defining new kinds of differentiable functions that are hard-equivalent to boolean functions, such as non-differentiable boolean majority. We propose `margin packing' as a potentially general technique for constructing differentiable functions that are hard-equivalent yet gradient-rich (and therefore backpropagate error to all their inputs). An advantage of $\partial\mathbb{B}$ nets is that we train the soft-net using efficient backpropagation on GPUs then `harden' to generate a learned discrete function that, unlike existing approaches to neural network binarization, has provably identical accuracy. + +$\partial\mathbb{B}$ nets, being ultimately of a discrete and logical nature, are easier to interpret compared to standard neural networks, for example generating propositional formulae that can be further analysed, either by symbolic simplification or verification by SAT solvers. These properties are important in safety-critical domains. In addition, $\partial\mathbb{B}$ nets at inference time are highly compact, due to 1-bit weights, and potentially cheap to evaluate, as they reduce to bit manipulation and integer arithmetic. These properties are important in resource-poor deployment environments, such as edge devices. Further, due to the differentiable nature of $\partial\mathbb{B}$ nets, they can be arbitrarily composed with standard neural nets (e.g. by embedding them within standard nets to introduce domain-specific logical bias). + +Preliminary experiments on three classification benchmarks demonstrate that $\partial\mathbb{B}$ nets can outperform multilayer perceptron networks, support vector machines, decision trees, and logistic regression. In terms of classification accuracy, the non-differentiable Tsetlin machine outperforms $\partial\mathbb{B}$ nets, which indicates room for futher improvements, e.g. by defining more expressive $\partial\mathbb{B}$ net layers (threshold functions with a learnable integer threshold, boolean decision lists etc.) and architectures (convolutional, regression nets, skip connections, attention etc.). In other words, this paper is only a first step towards exploring the space of differentiable nets that satisfy the requirement of hard-equivalence. + + +\subsubsection*{Acknowledgments} +Thanks to GitHub Next for sponsoring this research. And thanks to Pavel Augustinov, Richard Evans, Johan Rosenkilde, Max Schaefer, Ganesh Sittampalam, Tam\'{a}s Szab\'{o} and Albert Ziegler for helpful discussions and feedback. + +\bibliographystyle{iclr2021_conference} +\bibliography{db} + +\appendix + +\section*{Appendix} + +\section{Proofs} + +\begin{prop}\label{prop:not} + $\partial_{\neg}(x,y) \btright \neg (x \oplus y)$. +\begin{proof} + Table \ref{not-table} is the truth table of the boolean function $\neg (x \oplus w)$, where $h(x) = \operatorname{harden}(x)$. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\neg}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\neg}(x, y))$} + &\multicolumn{1}{c}{$\neg (h(y) \oplus h(x))$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2}, 1\right]$ & 1 & 1\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\neg}(x,y) \btright \neg (y \oplus x)$.}\label{not-table} + \end{table} +\end{proof} +\end{prop} + +\begin{lemma}\label{prop:augmented} + If a representative bit, $x_{i}$, is hard-equivalent to a target function, $g$, then so is the augmented bit, $z$. + \begin{proof} + As $x_{i}$ is representative then $\operatorname{harden}(x_{i}) = g(\operatorname{harden}({\bf x}))$. The augmented bit, $z$, is given by \eqref{eq:augmented-bit}: + \begin{equation*} + z = \begin{cases} + 1/2 + \bar{\bf x}\times|x_{i} - 1/2| & \text{if } x_{i} > 1/2 \\ + x_{i} + \bar{\bf x}\times|x_{i} - 1/2| & \text{otherwise.} + \end{cases} + \end{equation*} + In consequence, + \begin{equation*} + \operatorname{harden}(z) = \begin{cases} + 1 & \text{if } x > 1/2 \\ + 0 & \text{otherwise,} + \end{cases} + \end{equation*} + since $x_{i} > 1/2 \Rightarrow z > 1/2$ and $x_{i} \leq 1/2 \Rightarrow z \leq 1/2$. Hence, $\operatorname{harden}(z) = \operatorname{harden}(x_{i}) = g(\operatorname{harden}({\bf x}))$ + \end{proof} +\end{lemma} + + +\begin{prop}\label{prop:and} + $\partial_{\wedge}\!(x,y) \btright x \wedge y$. +\begin{proof} + Table \ref{and-table} is the truth table of the boolean function $x \wedge y$, where $h(x) = \operatorname{harden}(x)$.. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\wedge}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\wedge}(x, y))$} + &\multicolumn{1}{c}{$h(x) \wedge h(y)$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left(\frac{1}{4}, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left(\frac{1}{4}, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2}, 1\right]$ & 1 & 1\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\wedge}(x,y) \btright x \wedge y$.}\label{and-table} + \end{table} +\end{proof} +\end{prop} + +\begin{prop}\label{prop:or} + $\partial_{\vee}\!(x,y) \btright x \vee y$. +\begin{proof} + Table \ref{or-table} is the truth table of the boolean function $x \vee y$, where $h(x) = \operatorname{harden}(x)$.. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\vee}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\vee}(x, y))$} + &\multicolumn{1}{c}{$h(x) \vee h(y)$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left[0,\frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2},1\right]$ & 1 & 1\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\vee}(x,y) \btright x \vee y$.}\label{or-table} + \end{table} +\end{proof} +\end{prop} + +\begin{prop}\label{prop:implies} + $\partial_{\Rightarrow}\!(x,y) \btright x \Rightarrow y$. +\begin{proof} + Table \ref{implies-table} is the truth table of the boolean function $x \Rightarrow y$, where $h(x) = \operatorname{harden}(x)$.. + \begin{table}[h!] + \begin{center} + \begin{tabular}{ccccccc} + \multicolumn{1}{c}{$x$} &\multicolumn{1}{c}{$y$} &\multicolumn{1}{c}{$h(x)$} &\multicolumn{1}{c}{$h(y)$} &\multicolumn{1}{c}{$\partial_{\Rightarrow}(x, y)$} &\multicolumn{1}{c}{$h(\partial_{\Rightarrow}(x, y))$} + &\multicolumn{1}{c}{$h(x) \Rightarrow h(y)$} + \\ \hline \\ + $\left[0, \frac{1}{2}\right)$ & $\left[0, \frac{1}{2}\right)$ & 0 & 0 & $\left(\frac{1}{2}, 1\right]$ & 1 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left[0, \frac{1}{2}\right)$ &1 & 0 & $\left[0, \frac{1}{2}\right)$ & 0 & 0\\[0.1cm] + $\left[0, \frac{1}{2}\right)$ & $\left(\frac{1}{2}, 1\right]$ &0 & 1 & $\left(\frac{1}{2},1\right]$ & 1 & 0\\[0.1cm] + $\left(\frac{1}{2}, 1\right]$ & $\left(\frac{1}{2}, 1\right]$ &1 & 1 & $\left(\frac{1}{2}, \frac{7}{8}\right)$ & 1 & 0\\[0.1cm] + \end{tabular} + \end{center} + \caption{$\partial_{\Rightarrow}(x,y) \btright x \Rightarrow y$.}\label{implies-table} + \end{table} +\end{proof} +\end{prop} + +\begin{lemma} +\label{lem:maj} +Let $i$ = $\operatorname{majority-index}({\bf x})$, then the $i$th element of $\operatorname{sort}({\bf x})$ is hard-equivalent to boolean majority, i.e. $\operatorname{harden}(\operatorname{sort}({\bf x})[i]) = \operatorname{Maj}(\operatorname{harden}({\bf x}))$. +\begin{proof} +Let $h$ denote the number of bits that are high in ${\bf x} = [x_{1}, \dots, x_{n}]$. Then indices $\{j : n-h+1 \leq j \leq n\}$ are high in $\operatorname{sort}({\bf x})$. If the majority of bits are high, $h \geq \lfloor n/2 + 1 \rfloor$, then index $j=n - \lfloor n/2 + 1 \rfloor + 1 = n - \lfloor n/2 \rfloor = \lceil n/2 \rceil$ is high in $\operatorname{sort}({\bf x})$. $\operatorname{majority-index}$ selects index $i = \lceil n/2 \rceil$ and therefore $i=j$. Hence, if the majority of bits are high then $\operatorname{sort}({\bf x})[i]$ is high. Similarly, if the majority of bits are low, $h < \lfloor n/2 + 1 \rfloor$, then index $j=n - \lfloor n/2 + 1 \rfloor + 1 = n - \lfloor n/2 \rfloor = \lceil n/2 \rceil$ is low in $\operatorname{sort}({\bf x})$. Hence, if the majority of bits are low then $\operatorname{sort}({\bf x})[i]$ is low. + +Note that $h \geq \lfloor n/2 + 1 \rfloor$ implies that $\operatorname{Maj}(\operatorname{harden}({\bf x})) \geq \left\lfloor \frac{1}{2} + \frac{1}{n}\left(\frac{n}{2} + 1 - \frac{1}{2} \right) \right\rfloor \geq \left\lfloor 1 + \frac{1}{2n} \right\rfloor = 1$, and $h < \lfloor n/2 + 1 \rfloor$ implies that $\operatorname{Maj}(\operatorname{harden}({\bf x})) < \left\lfloor 1 + \frac{1}{2n} \right\rfloor = 0$. + +In consequence, $\operatorname{harden}(\operatorname{sort}({\bf x})[i]) = \operatorname{Maj}(\operatorname{harden}({\bf x}))$ for all $h \in [0,\dots, n]$. +\end{proof} +\end{lemma} + +\begin{theorem}\label{prop:majority} + $\partial\!\operatorname{Maj} \btright \operatorname{Maj}$. +\begin{proof} + $\partial\!\operatorname{Maj}$ augments the representative bit $x_{i} = \operatorname{sort}({\bf x})[\operatorname{majority-index}({\bf x})]$. By lemma \ref{lem:maj} the representative bit is $\btright \operatorname{Maj}(\operatorname{harden}({\bf x}))$. + By lemma \ref{prop:augmented}, the augmented bit, $\operatorname{augmented-bit}(\operatorname{sort}({\bf x}), \operatorname{majority-index}({\bf x}))$, is also $\btright\!\operatorname{Maj}(\operatorname{harden}({\bf x}))$. Hence $\partial\!\operatorname{Maj} \btright\!\operatorname{Maj}$. +\end{proof} +\end{theorem} + +\begin{prop}\label{prop:count} + $\partial\!\operatorname{count-hot} \btright \operatorname{count-hot}$. + \begin{proof} + Let $l$ denote the number of bits that are low in ${\bf x} = [x_{1},\dots,x_{n}]$, and let ${\bf y} = \partial\!\operatorname{count-hot}({\bf x})$. Then ${\bf y}[l+1]$ is high and any ${\bf y}[i]$, where $i \neq l+1$, is low. Let ${\bf z} = \operatorname{count-hot}(\operatorname{harden}({\bf x}))$. Then ${\bf z}[l+1]$ is high and any ${\bf z}[i]$, where $i \neq l+1$, is low. Hence, $\operatorname{harden}({\bf y}) = {\bf z}$, and therefore $\partial\!\operatorname{count-hot} \btright \operatorname{count-hot}$. + \end{proof} +\end{prop} + + +\end{document} + +\begin{comment} +Define +\begin{equation*} +\begin{aligned} +\partial\text{AND-LAYER}: [0,1]^{n \times m} \times [0,1]^{m} &\to [0,1]^{n}, \\ +({\bf W}, {\bf x}) &\mapsto [\partial_{\wedge}\operatorname{Neuron}({\bf W}_{1}, {\bf x}), \dots, \partial_{\wedge}\operatorname{Neuron}({\bf W}_{n}, {\bf x})] +\end{aligned} +\end{equation*} +\end{comment} diff --git a/docs/iclr2021_conference.bst b/docs/iclr2021_conference.bst new file mode 100644 index 0000000..149a48c --- /dev/null +++ b/docs/iclr2021_conference.bst @@ -0,0 +1,1440 @@ +%% File: `iclr2017.bst' +%% A copy of iclm2010.bst, which is a modification of `plainnl.bst' for use with natbib package +%% +%% Copyright 2010 Hal Daum\'e III +%% Modified by J. Frnkranz +%% - Changed labels from (X and Y, 2000) to (X & Y, 2000) +%% +%% Copyright 1993-2007 Patrick W Daly +%% Max-Planck-Institut f\"ur Sonnensystemforschung +%% Max-Planck-Str. 2 +%% D-37191 Katlenburg-Lindau +%% Germany +%% E-mail: daly@mps.mpg.de +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN +%% archives in directory macros/latex/base/lppl.txt; either +%% version 1 of the License, or any later version. +%% + % Version and source file information: + % \ProvidesFile{icml2010.mbs}[2007/11/26 1.93 (PWD)] + % + % BibTeX `plainnat' family + % version 0.99b for BibTeX versions 0.99a or later, + % for LaTeX versions 2.09 and 2e. + % + % For use with the `natbib.sty' package; emulates the corresponding + % member of the `plain' family, but with author-year citations. + % + % With version 6.0 of `natbib.sty', it may also be used for numerical + % citations, while retaining the commands \citeauthor, \citefullauthor, + % and \citeyear to print the corresponding information. + % + % For version 7.0 of `natbib.sty', the KEY field replaces missing + % authors/editors, and the date is left blank in \bibitem. + % + % Includes field EID for the sequence/citation number of electronic journals + % which is used instead of page numbers. + % + % Includes fields ISBN and ISSN. + % + % Includes field URL for Internet addresses. + % + % Includes field DOI for Digital Object Idenfifiers. + % + % Works best with the url.sty package of Donald Arseneau. + % + % Works with identical authors and year are further sorted by + % citation key, to preserve any natural sequence. + % +ENTRY + { address + author + booktitle + chapter + doi + eid + edition + editor + howpublished + institution + isbn + issn + journal + key + month + note + number + organization + pages + publisher + school + series + title + type + url + volume + year + } + {} + { label extra.label sort.label short.list } + +INTEGERS { output.state before.all mid.sentence after.sentence after.block } + +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} + +STRINGS { s t } + +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} + +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} + +FUNCTION {new.block.checka} +{ empty$ + 'skip$ + 'new.block + if$ +} + +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} + +FUNCTION {new.sentence.checka} +{ empty$ + 'skip$ + 'new.sentence + if$ +} + +FUNCTION {new.sentence.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.sentence + if$ +} + +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} + +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "\emph{" swap$ * "}" * } + if$ +} + +INTEGERS { nameptr namesleft numnames } + +FUNCTION {format.names} +{ 's := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr "{ff~}{vv~}{ll}{, jj}" format.name$ 't := + nameptr #1 > + { namesleft #1 > + { ", " * t * } + { numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {format.key} +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.authors} +{ author empty$ + { "" } + { author format.names } + if$ +} + +FUNCTION {format.editors} +{ editor empty$ + { "" } + { editor format.names + editor num.names$ #1 > + { " (eds.)" * } + { " (ed.)" * } + if$ + } + if$ +} + +FUNCTION {format.isbn} +{ isbn empty$ + { "" } + { new.block "ISBN " isbn * } + if$ +} + +FUNCTION {format.issn} +{ issn empty$ + { "" } + { new.block "ISSN " issn * } + if$ +} + +FUNCTION {format.url} +{ url empty$ + { "" } + { new.block "URL \url{" url * "}" * } + if$ +} + +FUNCTION {format.doi} +{ doi empty$ + { "" } + { new.block "\doi{" doi * "}" * } + if$ +} + +FUNCTION {format.title} +{ title empty$ + { "" } + { title "t" change.case$ } + if$ +} + +FUNCTION {format.full.names} +{'s := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}" format.name$ 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {author.editor.full} +{ author empty$ + { editor empty$ + { "" } + { editor format.full.names } + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {author.full} +{ author empty$ + { "" } + { author format.full.names } + if$ +} + +FUNCTION {editor.full} +{ editor empty$ + { "" } + { editor format.full.names } + if$ +} + +FUNCTION {make.full.names} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.full + { type$ "proceedings" = + 'editor.full + 'author.full + if$ + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[" write$ + label write$ + ")" make.full.names duplicate$ short.list = + { pop$ } + { * } + if$ + "]{" * write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {n.dashify} +{ 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {format.date} +{ year duplicate$ empty$ + { "empty year in " cite$ * warning$ + pop$ "" } + 'skip$ + if$ + month empty$ + 'skip$ + { month + " " * swap$ * + } + if$ + extra.label * +} + +FUNCTION {format.btitle} +{ title emphasize +} + +FUNCTION {tie.or.space.connect} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ * * +} + +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { "volume" volume tie.or.space.connect + series empty$ + 'skip$ + { " of " * series emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} + +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { output.state mid.sentence = + { "number" } + { "Number" } + if$ + number tie.or.space.connect + series empty$ + { "there's a number but no series in " cite$ * warning$ } + { " in " * series * } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {format.edition} +{ edition empty$ + { "" } + { output.state mid.sentence = + { edition "l" change.case$ " edition" * } + { edition "t" change.case$ " edition" * } + if$ + } + if$ +} + +INTEGERS { multiresult } + +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {format.pages} +{ pages empty$ + { "" } + { pages multi.page.check + { "pp.\ " pages n.dashify tie.or.space.connect } + { "pp.\ " pages tie.or.space.connect } + if$ + } + if$ +} + +FUNCTION {format.eid} +{ eid empty$ + { "" } + { "art." eid tie.or.space.connect } + if$ +} + +FUNCTION {format.vol.num.pages} +{ volume field.or.null + number empty$ + 'skip$ + { "\penalty0 (" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + pages empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.pages } + { ":\penalty0 " * pages n.dashify * } + if$ + } + if$ +} + +FUNCTION {format.vol.num.eid} +{ volume field.or.null + number empty$ + 'skip$ + { "\penalty0 (" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + eid empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.eid } + { ":\penalty0 " * eid * } + if$ + } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + 'format.pages + { type empty$ + { "chapter" } + { type "l" change.case$ } + if$ + chapter tie.or.space.connect + pages empty$ + 'skip$ + { ", " * format.pages * } + if$ + } + if$ +} + +FUNCTION {format.in.ed.booktitle} +{ booktitle empty$ + { "" } + { editor empty$ + { "In " booktitle emphasize * } + { "In " format.editors * ", " * booktitle emphasize * } + if$ + } + if$ +} + +FUNCTION {empty.misc.check} +{ author empty$ title empty$ howpublished empty$ + month empty$ year empty$ note empty$ + and and and and and + key empty$ not and + { "all relevant fields are empty in " cite$ * warning$ } + 'skip$ + if$ +} + +FUNCTION {format.thesis.type} +{ type empty$ + 'skip$ + { pop$ + type "t" change.case$ + } + if$ +} + +FUNCTION {format.tr.number} +{ type empty$ + { "Technical Report" } + 'type + if$ + number empty$ + { "t" change.case$ } + { number tie.or.space.connect } + if$ +} + +FUNCTION {format.article.crossref} +{ key empty$ + { journal empty$ + { "need key or journal for " cite$ * " to crossref " * crossref * + warning$ + "" + } + { "In \emph{" journal * "}" * } + if$ + } + { "In " } + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {format.book.crossref} +{ volume empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + "In " + } + { "Volume" volume tie.or.space.connect + " of " * + } + if$ + editor empty$ + editor field.or.null author field.or.null = + or + { key empty$ + { series empty$ + { "need editor, key, or series for " cite$ * " to crossref " * + crossref * warning$ + "" * + } + { "\emph{" * series * "}" * } + if$ + } + 'skip$ + if$ + } + 'skip$ + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {format.incoll.inproc.crossref} +{ editor empty$ + editor field.or.null author field.or.null = + or + { key empty$ + { booktitle empty$ + { "need editor, key, or booktitle for " cite$ * " to crossref " * + crossref * warning$ + "" + } + { "In \emph{" booktitle * "}" * } + if$ + } + { "In " } + if$ + } + { "In " } + if$ + " \citet{" * crossref * "}" * +} + +FUNCTION {article} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { journal emphasize "journal" output.check + eid empty$ + { format.vol.num.pages output } + { format.vol.num.eid output } + if$ + format.date "year" output.check + } + { format.article.crossref output.nonnull + eid empty$ + { format.pages output } + { format.eid output } + if$ + } + if$ + format.issn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {book} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.date "year" output.check + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {booklet} +{ output.bibitem + format.authors output + author format.key output + new.block + format.title "title" output.check + howpublished address new.block.checkb + howpublished output + address output + format.date output + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {inbook} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + format.chapter.pages "chapter and pages" output.check + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { format.chapter.pages "chapter and pages" output.check + new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.date "year" output.check + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {incollection} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.chapter.pages output + new.sentence + publisher "publisher" output.check + address output + format.edition output + format.date "year" output.check + } + { format.incoll.inproc.crossref output.nonnull + format.chapter.pages output + } + if$ + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {inproceedings} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.pages output + address empty$ + { organization publisher new.sentence.checkb + organization output + publisher output + format.date "year" output.check + } + { address output.nonnull + format.date "year" output.check + new.sentence + organization output + publisher output + } + if$ + } + { format.incoll.inproc.crossref output.nonnull + format.pages output + } + if$ + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {conference} { inproceedings } + +FUNCTION {manual} +{ output.bibitem + format.authors output + author format.key output + new.block + format.btitle "title" output.check + organization address new.block.checkb + organization output + address output + format.edition output + format.date output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {mastersthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + "Master's thesis" format.thesis.type output.nonnull + school "school" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {misc} +{ output.bibitem + format.authors output + author format.key output + title howpublished new.block.checkb + format.title output + howpublished new.block.checka + howpublished output + format.date output + format.issn output + format.url output + new.block + note output + fin.entry + empty.misc.check +} + +FUNCTION {phdthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.btitle "title" output.check + new.block + "PhD thesis" format.thesis.type output.nonnull + school "school" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {proceedings} +{ output.bibitem + format.editors output + editor format.key output + new.block + format.btitle "title" output.check + format.bvolume output + format.number.series output + address output + format.date "year" output.check + new.sentence + organization output + publisher output + format.isbn output + format.doi output + format.url output + new.block + note output + fin.entry +} + +FUNCTION {techreport} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + format.tr.number output.nonnull + institution "institution" output.check + address output + format.date "year" output.check + format.url output + new.block + note output + fin.entry +} + +FUNCTION {unpublished} +{ output.bibitem + format.authors "author" output.check + author format.key output + new.block + format.title "title" output.check + new.block + note "note" output.check + format.date output + format.url output + fin.entry +} + +FUNCTION {default.type} { misc } + + +MACRO {jan} {"January"} + +MACRO {feb} {"February"} + +MACRO {mar} {"March"} + +MACRO {apr} {"April"} + +MACRO {may} {"May"} + +MACRO {jun} {"June"} + +MACRO {jul} {"July"} + +MACRO {aug} {"August"} + +MACRO {sep} {"September"} + +MACRO {oct} {"October"} + +MACRO {nov} {"November"} + +MACRO {dec} {"December"} + + + +MACRO {acmcs} {"ACM Computing Surveys"} + +MACRO {acta} {"Acta Informatica"} + +MACRO {cacm} {"Communications of the ACM"} + +MACRO {ibmjrd} {"IBM Journal of Research and Development"} + +MACRO {ibmsj} {"IBM Systems Journal"} + +MACRO {ieeese} {"IEEE Transactions on Software Engineering"} + +MACRO {ieeetc} {"IEEE Transactions on Computers"} + +MACRO {ieeetcad} + {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"} + +MACRO {ipl} {"Information Processing Letters"} + +MACRO {jacm} {"Journal of the ACM"} + +MACRO {jcss} {"Journal of Computer and System Sciences"} + +MACRO {scp} {"Science of Computer Programming"} + +MACRO {sicomp} {"SIAM Journal on Computing"} + +MACRO {tocs} {"ACM Transactions on Computer Systems"} + +MACRO {tods} {"ACM Transactions on Database Systems"} + +MACRO {tog} {"ACM Transactions on Graphics"} + +MACRO {toms} {"ACM Transactions on Mathematical Software"} + +MACRO {toois} {"ACM Transactions on Office Information Systems"} + +MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"} + +MACRO {tcs} {"Theoretical Computer Science"} + + +READ + +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} + +INTEGERS { len } + +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} + +FUNCTION {format.lab.names} +{ 's := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ " et~al." * } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { " et~al." * } + { " \& " * s #2 "{vv~}{ll}" format.name$ * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.key.organization.label} +{ author empty$ + { key empty$ + { organization empty$ + { cite$ #1 #3 substring$ } + { "The " #4 organization chop.word #3 text.prefix$ } + if$ + } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.organization.label} +{ editor empty$ + { key empty$ + { organization empty$ + { cite$ #1 #3 substring$ } + { "The " #4 organization chop.word #3 text.prefix$ } + if$ + } + 'key + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.short.authors} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.organization.label + { type$ "manual" = + 'author.key.organization.label + 'author.key.label + if$ + } + if$ + } + if$ + 'short.list := +} + +FUNCTION {calc.label} +{ calc.short.authors + short.list + "(" + * + year duplicate$ empty$ + short.list key field.or.null = or + { pop$ "" } + 'skip$ + if$ + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { + s nameptr "{vv{ } }{ll{ }}{ ff{ }}{ jj{ }}" format.name$ 't := + nameptr #1 > + { + " " * + namesleft #1 = t "others" = and + { "zzzzz" * } + { numnames #2 > nameptr #2 = and + { "zz" * year field.or.null * " " * } + 'skip$ + if$ + t sortify * + } + if$ + } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} + +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.organization.sort} +{ author empty$ + { organization empty$ + { key empty$ + { "to sort, need author, organization, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { "The " #4 organization chop.word sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {editor.organization.sort} +{ editor empty$ + { organization empty$ + { key empty$ + { "to sort, need editor, organization, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { "The " #4 organization chop.word sortify } + if$ + } + { editor sort.format.names } + if$ +} + + +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.organization.sort + { type$ "manual" = + 'author.organization.sort + 'author.sort + if$ + } + if$ + } + if$ + " " + * + year field.or.null sortify + * + " " + * + cite$ + * + #1 entry.max$ substring$ + 'sort.label := + sort.label * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} + +SORT + +STRINGS { longest.label last.label next.extra } + +INTEGERS { longest.label.width last.extra.num number.label } + +FUNCTION {initialize.longest.label} +{ "" 'longest.label := + #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'longest.label.width := + #0 'last.extra.num := + #0 'number.label := +} + +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ + number.label #1 + 'number.label := +} + +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + extra.label 'next.extra := + extra.label + duplicate$ empty$ + 'skip$ + { "{\natexlab{" swap$ * "}}" * } + if$ + 'extra.label := + label extra.label * 'label := +} + +EXECUTE {initialize.longest.label} + +ITERATE {forward.pass} + +REVERSE {reverse.pass} + +FUNCTION {bib.sort.order} +{ sort.label 'sort.key$ := +} + +ITERATE {bib.sort.order} + +SORT + +FUNCTION {begin.bib} +{ preamble$ empty$ + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" number.label int.to.str$ * "}" * + write$ newline$ + "\providecommand{\natexlab}[1]{#1}" + write$ newline$ + "\providecommand{\url}[1]{\texttt{#1}}" + write$ newline$ + "\expandafter\ifx\csname urlstyle\endcsname\relax" + write$ newline$ + " \providecommand{\doi}[1]{doi: #1}\else" + write$ newline$ + " \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi" + write$ newline$ +} + +EXECUTE {begin.bib} + +EXECUTE {init.state.consts} + +ITERATE {call.type$} + +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} + +EXECUTE {end.bib} diff --git a/docs/iclr2021_conference.sty b/docs/iclr2021_conference.sty new file mode 100644 index 0000000..f68d5dc --- /dev/null +++ b/docs/iclr2021_conference.sty @@ -0,0 +1,246 @@ +%%%% ICLR Macros (LaTex) +%%%% Adapted by Hugo Larochelle from the NIPS stylefile Macros +%%%% Style File +%%%% Dec 12, 1990 Rev Aug 14, 1991; Sept, 1995; April, 1997; April, 1999; October 2014 + +% This file can be used with Latex2e whether running in main mode, or +% 2.09 compatibility mode. +% +% If using main mode, you need to include the commands +% \documentclass{article} +% \usepackage{iclr14submit_e,times} +% + +% Change the overall width of the page. If these parameters are +% changed, they will require corresponding changes in the +% maketitle section. +% +\usepackage{eso-pic} % used by \AddToShipoutPicture +\RequirePackage{fancyhdr} +\RequirePackage{natbib} + +% modification to natbib citations +\setcitestyle{authoryear,round,citesep={;},aysep={,},yysep={;}} + +\renewcommand{\topfraction}{0.95} % let figure take up nearly whole page +\renewcommand{\textfraction}{0.05} % let figure take up nearly whole page + +% Define iclrfinal, set to true if iclrfinalcopy is defined +\newif\ificlrfinal +\iclrfinalfalse +\def\iclrfinalcopy{\iclrfinaltrue} +\font\iclrtenhv = phvb at 8pt + +% Specify the dimensions of each page + +\setlength{\paperheight}{11in} +\setlength{\paperwidth}{8.5in} + + +\oddsidemargin .5in % Note \oddsidemargin = \evensidemargin +\evensidemargin .5in +\marginparwidth 0.07 true in +%\marginparwidth 0.75 true in +%\topmargin 0 true pt % Nominal distance from top of page to top of +%\topmargin 0.125in +\topmargin -0.625in +\addtolength{\headsep}{0.25in} +\textheight 9.0 true in % Height of text (including footnotes & figures) +\textwidth 5.5 true in % Width of text line. +\widowpenalty=10000 +\clubpenalty=10000 + +% \thispagestyle{empty} \pagestyle{empty} +\flushbottom \sloppy + +% We're never going to need a table of contents, so just flush it to +% save space --- suggested by drstrip@sandia-2 +\def\addcontentsline#1#2#3{} + +% Title stuff, taken from deproc. +\def\maketitle{\par +\begingroup + \def\thefootnote{\fnsymbol{footnote}} + \def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}} % for perfect author + % name centering +% The footnote-mark was overlapping the footnote-text, +% added the following to fix this problem (MK) + \long\def\@makefntext##1{\parindent 1em\noindent + \hbox to1.8em{\hss $\m@th ^{\@thefnmark}$}##1} + \@maketitle \@thanks +\endgroup +\setcounter{footnote}{0} +\let\maketitle\relax \let\@maketitle\relax +\gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax} + +% The toptitlebar has been raised to top-justify the first page + +\usepackage{fancyhdr} +\pagestyle{fancy} +\fancyhead{} + +% Title (includes both anonimized and non-anonimized versions) +\def\@maketitle{\vbox{\hsize\textwidth +%\linewidth\hsize \vskip 0.1in \toptitlebar \centering +{\LARGE\sc \@title\par} +%\bottomtitlebar % \vskip 0.1in % minus +\ificlrfinal + %\lhead{Published as a conference paper at ICLR 2021} + \lhead{April 2023. DRAFT 1.1.} + \def\And{\end{tabular}\hfil\linebreak[0]\hfil + \begin{tabular}[t]{l}\bf\rule{\z@}{24pt}\ignorespaces}% + \def\AND{\end{tabular}\hfil\linebreak[4]\hfil + \begin{tabular}[t]{l}\bf\rule{\z@}{24pt}\ignorespaces}% + \begin{tabular}[t]{l}\bf\rule{\z@}{24pt}\@author\end{tabular}% +\else + \lhead{Under review as a conference paper at ICLR 2021} + \def\And{\end{tabular}\hfil\linebreak[0]\hfil + \begin{tabular}[t]{l}\bf\rule{\z@}{24pt}\ignorespaces}% + \def\AND{\end{tabular}\hfil\linebreak[4]\hfil + \begin{tabular}[t]{l}\bf\rule{\z@}{24pt}\ignorespaces}% + \begin{tabular}[t]{l}\bf\rule{\z@}{24pt}Anonymous authors\\Paper under double-blind review\end{tabular}% +\fi +\vskip 0.3in minus 0.1in}} + +\renewenvironment{abstract}{\vskip.075in\centerline{\large\sc +Abstract}\vspace{0.5ex}\begin{quote}}{\par\end{quote}\vskip 1ex} + +% sections with less space +\def\section{\@startsection {section}{1}{\z@}{-2.0ex plus + -0.5ex minus -.2ex}{1.5ex plus 0.3ex +minus0.2ex}{\large\sc\raggedright}} + +\def\subsection{\@startsection{subsection}{2}{\z@}{-1.8ex plus +-0.5ex minus -.2ex}{0.8ex plus .2ex}{\normalsize\sc\raggedright}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-1.5ex +plus -0.5ex minus -.2ex}{0.5ex plus +.2ex}{\normalsize\sc\raggedright}} +\def\paragraph{\@startsection{paragraph}{4}{\z@}{1.5ex plus +0.5ex minus .2ex}{-1em}{\normalsize\bf}} +\def\subparagraph{\@startsection{subparagraph}{5}{\z@}{1.5ex plus + 0.5ex minus .2ex}{-1em}{\normalsize\sc}} +\def\subsubsubsection{\vskip +5pt{\noindent\normalsize\rm\raggedright}} + + +% Footnotes +\footnotesep 6.65pt % +\skip\footins 9pt plus 4pt minus 2pt +\def\footnoterule{\kern-3pt \hrule width 12pc \kern 2.6pt } +\setcounter{footnote}{0} + +% Lists and paragraphs +\parindent 0pt +\topsep 4pt plus 1pt minus 2pt +\partopsep 1pt plus 0.5pt minus 0.5pt +\itemsep 2pt plus 1pt minus 0.5pt +\parsep 2pt plus 1pt minus 0.5pt +\parskip .5pc + + +%\leftmargin2em +\leftmargin3pc +\leftmargini\leftmargin \leftmarginii 2em +\leftmarginiii 1.5em \leftmarginiv 1.0em \leftmarginv .5em + +%\labelsep \labelsep 5pt + +\def\@listi{\leftmargin\leftmargini} +\def\@listii{\leftmargin\leftmarginii + \labelwidth\leftmarginii\advance\labelwidth-\labelsep + \topsep 2pt plus 1pt minus 0.5pt + \parsep 1pt plus 0.5pt minus 0.5pt + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii\advance\labelwidth-\labelsep + \topsep 1pt plus 0.5pt minus 0.5pt + \parsep \z@ \partopsep 0.5pt plus 0pt minus 0.5pt + \itemsep \topsep} +\def\@listiv{\leftmargin\leftmarginiv + \labelwidth\leftmarginiv\advance\labelwidth-\labelsep} +\def\@listv{\leftmargin\leftmarginv + \labelwidth\leftmarginv\advance\labelwidth-\labelsep} +\def\@listvi{\leftmargin\leftmarginvi + \labelwidth\leftmarginvi\advance\labelwidth-\labelsep} + +\abovedisplayskip 7pt plus2pt minus5pt% +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip 0pt plus3pt% +\belowdisplayshortskip 4pt plus3pt minus3pt% + +% Less leading in most fonts (due to the narrow columns) +% The choices were between 1-pt and 1.5-pt leading +%\def\@normalsize{\@setsize\normalsize{11pt}\xpt\@xpt} % got rid of @ (MK) +\def\normalsize{\@setsize\normalsize{11pt}\xpt\@xpt} +\def\small{\@setsize\small{10pt}\ixpt\@ixpt} +\def\footnotesize{\@setsize\footnotesize{10pt}\ixpt\@ixpt} +\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt} +\def\tiny{\@setsize\tiny{7pt}\vipt\@vipt} +\def\large{\@setsize\large{14pt}\xiipt\@xiipt} +\def\Large{\@setsize\Large{16pt}\xivpt\@xivpt} +\def\LARGE{\@setsize\LARGE{20pt}\xviipt\@xviipt} +\def\huge{\@setsize\huge{23pt}\xxpt\@xxpt} +\def\Huge{\@setsize\Huge{28pt}\xxvpt\@xxvpt} + +\def\toptitlebar{\hrule height4pt\vskip .25in\vskip-\parskip} + +\def\bottomtitlebar{\vskip .29in\vskip-\parskip\hrule height1pt\vskip +.09in} % +%Reduced second vskip to compensate for adding the strut in \@author + + +%% % Vertical Ruler +%% % This code is, largely, from the CVPR 2010 conference style file +%% % ----- define vruler +%% \makeatletter +%% \newbox\iclrrulerbox +%% \newcount\iclrrulercount +%% \newdimen\iclrruleroffset +%% \newdimen\cv@lineheight +%% \newdimen\cv@boxheight +%% \newbox\cv@tmpbox +%% \newcount\cv@refno +%% \newcount\cv@tot +%% % NUMBER with left flushed zeros \fillzeros[] +%% \newcount\cv@tmpc@ \newcount\cv@tmpc +%% \def\fillzeros[#1]#2{\cv@tmpc@=#2\relax\ifnum\cv@tmpc@<0\cv@tmpc@=-\cv@tmpc@\fi +%% \cv@tmpc=1 % +%% \loop\ifnum\cv@tmpc@<10 \else \divide\cv@tmpc@ by 10 \advance\cv@tmpc by 1 \fi +%% \ifnum\cv@tmpc@=10\relax\cv@tmpc@=11\relax\fi \ifnum\cv@tmpc@>10 \repeat +%% \ifnum#2<0\advance\cv@tmpc1\relax-\fi +%% \loop\ifnum\cv@tmpc<#1\relax0\advance\cv@tmpc1\relax\fi \ifnum\cv@tmpc<#1 \repeat +%% \cv@tmpc@=#2\relax\ifnum\cv@tmpc@<0\cv@tmpc@=-\cv@tmpc@\fi \relax\the\cv@tmpc@}% +%% % \makevruler[][][][][] +%% \def\makevruler[#1][#2][#3][#4][#5]{\begingroup\offinterlineskip +%% \textheight=#5\vbadness=10000\vfuzz=120ex\overfullrule=0pt% +%% \global\setbox\iclrrulerbox=\vbox to \textheight{% +%% {\parskip=0pt\hfuzz=150em\cv@boxheight=\textheight +%% \cv@lineheight=#1\global\iclrrulercount=#2% +%% \cv@tot\cv@boxheight\divide\cv@tot\cv@lineheight\advance\cv@tot2% +%% \cv@refno1\vskip-\cv@lineheight\vskip1ex% +%% \loop\setbox\cv@tmpbox=\hbox to0cm{{\iclrtenhv\hfil\fillzeros[#4]\iclrrulercount}}% +%% \ht\cv@tmpbox\cv@lineheight\dp\cv@tmpbox0pt\box\cv@tmpbox\break +%% \advance\cv@refno1\global\advance\iclrrulercount#3\relax +%% \ifnum\cv@refno<\cv@tot\repeat}}\endgroup}% +%% \makeatother +%% % ----- end of vruler + +%% % \makevruler[][][][][] +%% \def\iclrruler#1{\makevruler[12pt][#1][1][3][0.993\textheight]\usebox{\iclrrulerbox}} +%% \AddToShipoutPicture{% +%% \ificlrfinal\else +%% \iclrruleroffset=\textheight +%% \advance\iclrruleroffset by -3.7pt +%% \color[rgb]{.7,.7,.7} +%% \AtTextUpperLeft{% +%% \put(\LenToUnit{-35pt},\LenToUnit{-\iclrruleroffset}){%left ruler +%% \iclrruler{\iclrrulercount}} +%% } +%% \fi +%% } +%%% To add a vertical bar on the side +%\AddToShipoutPicture{ +%\AtTextLowerLeft{ +%\hspace*{-1.8cm} +%\colorbox[rgb]{0.7,0.7,0.7}{\small \parbox[b][\textheight]{0.1cm}{}}} +%} diff --git a/docs/logic-gates.png b/docs/logic-gates.png new file mode 100644 index 0000000..26a5c77 Binary files /dev/null and b/docs/logic-gates.png differ diff --git a/docs/majority-gates.png b/docs/majority-gates.png new file mode 100644 index 0000000..abf3e45 Binary files /dev/null and b/docs/majority-gates.png differ diff --git a/docs/margin-trick.png b/docs/margin-trick.png new file mode 100644 index 0000000..2629388 Binary files /dev/null and b/docs/margin-trick.png differ diff --git a/docs/math_commands.tex b/docs/math_commands.tex new file mode 100644 index 0000000..0668f93 --- /dev/null +++ b/docs/math_commands.tex @@ -0,0 +1,508 @@ +%%%%% NEW MATH DEFINITIONS %%%%% + +\usepackage{amsmath,amsfonts,bm} + +% Mark sections of captions for referring to divisions of figures +\newcommand{\figleft}{{\em (Left)}} +\newcommand{\figcenter}{{\em (Center)}} +\newcommand{\figright}{{\em (Right)}} +\newcommand{\figtop}{{\em (Top)}} +\newcommand{\figbottom}{{\em (Bottom)}} +\newcommand{\captiona}{{\em (a)}} +\newcommand{\captionb}{{\em (b)}} +\newcommand{\captionc}{{\em (c)}} +\newcommand{\captiond}{{\em (d)}} + +% Highlight a newly defined term +\newcommand{\newterm}[1]{{\bf #1}} + + +% Figure reference, lower-case. +\def\figref#1{figure~\ref{#1}} +% Figure reference, capital. For start of sentence +\def\Figref#1{Figure~\ref{#1}} +\def\twofigref#1#2{figures \ref{#1} and \ref{#2}} +\def\quadfigref#1#2#3#4{figures \ref{#1}, \ref{#2}, \ref{#3} and \ref{#4}} +% Section reference, lower-case. +\def\secref#1{section~\ref{#1}} +% Section reference, capital. +\def\Secref#1{Section~\ref{#1}} +% Reference to two sections. +\def\twosecrefs#1#2{sections \ref{#1} and \ref{#2}} +% Reference to three sections. +\def\secrefs#1#2#3{sections \ref{#1}, \ref{#2} and \ref{#3}} +% Reference to an equation, lower-case. +\def\eqref#1{equation~\ref{#1}} +% Reference to an equation, upper case +\def\Eqref#1{Equation~\ref{#1}} +% A raw reference to an equation---avoid using if possible +\def\plaineqref#1{\ref{#1}} +% Reference to a chapter, lower-case. +\def\chapref#1{chapter~\ref{#1}} +% Reference to an equation, upper case. +\def\Chapref#1{Chapter~\ref{#1}} +% Reference to a range of chapters +\def\rangechapref#1#2{chapters\ref{#1}--\ref{#2}} +% Reference to an algorithm, lower-case. +\def\algref#1{algorithm~\ref{#1}} +% Reference to an algorithm, upper case. +\def\Algref#1{Algorithm~\ref{#1}} +\def\twoalgref#1#2{algorithms \ref{#1} and \ref{#2}} +\def\Twoalgref#1#2{Algorithms \ref{#1} and \ref{#2}} +% Reference to a part, lower case +\def\partref#1{part~\ref{#1}} +% Reference to a part, upper case +\def\Partref#1{Part~\ref{#1}} +\def\twopartref#1#2{parts \ref{#1} and \ref{#2}} + +\def\ceil#1{\lceil #1 \rceil} +\def\floor#1{\lfloor #1 \rfloor} +\def\1{\bm{1}} +\newcommand{\train}{\mathcal{D}} +\newcommand{\valid}{\mathcal{D_{\mathrm{valid}}}} +\newcommand{\test}{\mathcal{D_{\mathrm{test}}}} + +\def\eps{{\epsilon}} + + +% Random variables +\def\reta{{\textnormal{$\eta$}}} +\def\ra{{\textnormal{a}}} +\def\rb{{\textnormal{b}}} +\def\rc{{\textnormal{c}}} +\def\rd{{\textnormal{d}}} +\def\re{{\textnormal{e}}} +\def\rf{{\textnormal{f}}} +\def\rg{{\textnormal{g}}} +\def\rh{{\textnormal{h}}} +\def\ri{{\textnormal{i}}} +\def\rj{{\textnormal{j}}} +\def\rk{{\textnormal{k}}} +\def\rl{{\textnormal{l}}} +% rm is already a command, just don't name any random variables m +\def\rn{{\textnormal{n}}} +\def\ro{{\textnormal{o}}} +\def\rp{{\textnormal{p}}} +\def\rq{{\textnormal{q}}} +\def\rr{{\textnormal{r}}} +\def\rs{{\textnormal{s}}} +\def\rt{{\textnormal{t}}} +\def\ru{{\textnormal{u}}} +\def\rv{{\textnormal{v}}} +\def\rw{{\textnormal{w}}} +\def\rx{{\textnormal{x}}} +\def\ry{{\textnormal{y}}} +\def\rz{{\textnormal{z}}} + +% Random vectors +\def\rvepsilon{{\mathbf{\epsilon}}} +\def\rvtheta{{\mathbf{\theta}}} +\def\rva{{\mathbf{a}}} +\def\rvb{{\mathbf{b}}} +\def\rvc{{\mathbf{c}}} +\def\rvd{{\mathbf{d}}} +\def\rve{{\mathbf{e}}} +\def\rvf{{\mathbf{f}}} +\def\rvg{{\mathbf{g}}} +\def\rvh{{\mathbf{h}}} +\def\rvu{{\mathbf{i}}} +\def\rvj{{\mathbf{j}}} +\def\rvk{{\mathbf{k}}} +\def\rvl{{\mathbf{l}}} +\def\rvm{{\mathbf{m}}} +\def\rvn{{\mathbf{n}}} +\def\rvo{{\mathbf{o}}} +\def\rvp{{\mathbf{p}}} +\def\rvq{{\mathbf{q}}} +\def\rvr{{\mathbf{r}}} +\def\rvs{{\mathbf{s}}} +\def\rvt{{\mathbf{t}}} +\def\rvu{{\mathbf{u}}} +\def\rvv{{\mathbf{v}}} +\def\rvw{{\mathbf{w}}} +\def\rvx{{\mathbf{x}}} +\def\rvy{{\mathbf{y}}} +\def\rvz{{\mathbf{z}}} + +% Elements of random vectors +\def\erva{{\textnormal{a}}} +\def\ervb{{\textnormal{b}}} +\def\ervc{{\textnormal{c}}} +\def\ervd{{\textnormal{d}}} +\def\erve{{\textnormal{e}}} +\def\ervf{{\textnormal{f}}} +\def\ervg{{\textnormal{g}}} +\def\ervh{{\textnormal{h}}} +\def\ervi{{\textnormal{i}}} +\def\ervj{{\textnormal{j}}} +\def\ervk{{\textnormal{k}}} +\def\ervl{{\textnormal{l}}} +\def\ervm{{\textnormal{m}}} +\def\ervn{{\textnormal{n}}} +\def\ervo{{\textnormal{o}}} +\def\ervp{{\textnormal{p}}} +\def\ervq{{\textnormal{q}}} +\def\ervr{{\textnormal{r}}} +\def\ervs{{\textnormal{s}}} +\def\ervt{{\textnormal{t}}} +\def\ervu{{\textnormal{u}}} +\def\ervv{{\textnormal{v}}} +\def\ervw{{\textnormal{w}}} +\def\ervx{{\textnormal{x}}} +\def\ervy{{\textnormal{y}}} +\def\ervz{{\textnormal{z}}} + +% Random matrices +\def\rmA{{\mathbf{A}}} +\def\rmB{{\mathbf{B}}} +\def\rmC{{\mathbf{C}}} +\def\rmD{{\mathbf{D}}} +\def\rmE{{\mathbf{E}}} +\def\rmF{{\mathbf{F}}} +\def\rmG{{\mathbf{G}}} +\def\rmH{{\mathbf{H}}} +\def\rmI{{\mathbf{I}}} +\def\rmJ{{\mathbf{J}}} +\def\rmK{{\mathbf{K}}} +\def\rmL{{\mathbf{L}}} +\def\rmM{{\mathbf{M}}} +\def\rmN{{\mathbf{N}}} +\def\rmO{{\mathbf{O}}} +\def\rmP{{\mathbf{P}}} +\def\rmQ{{\mathbf{Q}}} +\def\rmR{{\mathbf{R}}} +\def\rmS{{\mathbf{S}}} +\def\rmT{{\mathbf{T}}} +\def\rmU{{\mathbf{U}}} +\def\rmV{{\mathbf{V}}} +\def\rmW{{\mathbf{W}}} +\def\rmX{{\mathbf{X}}} +\def\rmY{{\mathbf{Y}}} +\def\rmZ{{\mathbf{Z}}} + +% Elements of random matrices +\def\ermA{{\textnormal{A}}} +\def\ermB{{\textnormal{B}}} +\def\ermC{{\textnormal{C}}} +\def\ermD{{\textnormal{D}}} +\def\ermE{{\textnormal{E}}} +\def\ermF{{\textnormal{F}}} +\def\ermG{{\textnormal{G}}} +\def\ermH{{\textnormal{H}}} +\def\ermI{{\textnormal{I}}} +\def\ermJ{{\textnormal{J}}} +\def\ermK{{\textnormal{K}}} +\def\ermL{{\textnormal{L}}} +\def\ermM{{\textnormal{M}}} +\def\ermN{{\textnormal{N}}} +\def\ermO{{\textnormal{O}}} +\def\ermP{{\textnormal{P}}} +\def\ermQ{{\textnormal{Q}}} +\def\ermR{{\textnormal{R}}} +\def\ermS{{\textnormal{S}}} +\def\ermT{{\textnormal{T}}} +\def\ermU{{\textnormal{U}}} +\def\ermV{{\textnormal{V}}} +\def\ermW{{\textnormal{W}}} +\def\ermX{{\textnormal{X}}} +\def\ermY{{\textnormal{Y}}} +\def\ermZ{{\textnormal{Z}}} + +% Vectors +\def\vzero{{\bm{0}}} +\def\vone{{\bm{1}}} +\def\vmu{{\bm{\mu}}} +\def\vtheta{{\bm{\theta}}} +\def\va{{\bm{a}}} +\def\vb{{\bm{b}}} +\def\vc{{\bm{c}}} +\def\vd{{\bm{d}}} +\def\ve{{\bm{e}}} +\def\vf{{\bm{f}}} +\def\vg{{\bm{g}}} +\def\vh{{\bm{h}}} +\def\vi{{\bm{i}}} +\def\vj{{\bm{j}}} +\def\vk{{\bm{k}}} +\def\vl{{\bm{l}}} +\def\vm{{\bm{m}}} +\def\vn{{\bm{n}}} +\def\vo{{\bm{o}}} +\def\vp{{\bm{p}}} +\def\vq{{\bm{q}}} +\def\vr{{\bm{r}}} +\def\vs{{\bm{s}}} +\def\vt{{\bm{t}}} +\def\vu{{\bm{u}}} +\def\vv{{\bm{v}}} +\def\vw{{\bm{w}}} +\def\vx{{\bm{x}}} +\def\vy{{\bm{y}}} +\def\vz{{\bm{z}}} + +% Elements of vectors +\def\evalpha{{\alpha}} +\def\evbeta{{\beta}} +\def\evepsilon{{\epsilon}} +\def\evlambda{{\lambda}} +\def\evomega{{\omega}} +\def\evmu{{\mu}} +\def\evpsi{{\psi}} +\def\evsigma{{\sigma}} +\def\evtheta{{\theta}} +\def\eva{{a}} +\def\evb{{b}} +\def\evc{{c}} +\def\evd{{d}} +\def\eve{{e}} +\def\evf{{f}} +\def\evg{{g}} +\def\evh{{h}} +\def\evi{{i}} +\def\evj{{j}} +\def\evk{{k}} +\def\evl{{l}} +\def\evm{{m}} +\def\evn{{n}} +\def\evo{{o}} +\def\evp{{p}} +\def\evq{{q}} +\def\evr{{r}} +\def\evs{{s}} +\def\evt{{t}} +\def\evu{{u}} +\def\evv{{v}} +\def\evw{{w}} +\def\evx{{x}} +\def\evy{{y}} +\def\evz{{z}} + +% Matrix +\def\mA{{\bm{A}}} +\def\mB{{\bm{B}}} +\def\mC{{\bm{C}}} +\def\mD{{\bm{D}}} +\def\mE{{\bm{E}}} +\def\mF{{\bm{F}}} +\def\mG{{\bm{G}}} +\def\mH{{\bm{H}}} +\def\mI{{\bm{I}}} +\def\mJ{{\bm{J}}} +\def\mK{{\bm{K}}} +\def\mL{{\bm{L}}} +\def\mM{{\bm{M}}} +\def\mN{{\bm{N}}} +\def\mO{{\bm{O}}} +\def\mP{{\bm{P}}} +\def\mQ{{\bm{Q}}} +\def\mR{{\bm{R}}} +\def\mS{{\bm{S}}} +\def\mT{{\bm{T}}} +\def\mU{{\bm{U}}} +\def\mV{{\bm{V}}} +\def\mW{{\bm{W}}} +\def\mX{{\bm{X}}} +\def\mY{{\bm{Y}}} +\def\mZ{{\bm{Z}}} +\def\mBeta{{\bm{\beta}}} +\def\mPhi{{\bm{\Phi}}} +\def\mLambda{{\bm{\Lambda}}} +\def\mSigma{{\bm{\Sigma}}} + +% Tensor +\DeclareMathAlphabet{\mathsfit}{\encodingdefault}{\sfdefault}{m}{sl} +\SetMathAlphabet{\mathsfit}{bold}{\encodingdefault}{\sfdefault}{bx}{n} +\newcommand{\tens}[1]{\bm{\mathsfit{#1}}} +\def\tA{{\tens{A}}} +\def\tB{{\tens{B}}} +\def\tC{{\tens{C}}} +\def\tD{{\tens{D}}} +\def\tE{{\tens{E}}} +\def\tF{{\tens{F}}} +\def\tG{{\tens{G}}} +\def\tH{{\tens{H}}} +\def\tI{{\tens{I}}} +\def\tJ{{\tens{J}}} +\def\tK{{\tens{K}}} +\def\tL{{\tens{L}}} +\def\tM{{\tens{M}}} +\def\tN{{\tens{N}}} +\def\tO{{\tens{O}}} +\def\tP{{\tens{P}}} +\def\tQ{{\tens{Q}}} +\def\tR{{\tens{R}}} +\def\tS{{\tens{S}}} +\def\tT{{\tens{T}}} +\def\tU{{\tens{U}}} +\def\tV{{\tens{V}}} +\def\tW{{\tens{W}}} +\def\tX{{\tens{X}}} +\def\tY{{\tens{Y}}} +\def\tZ{{\tens{Z}}} + + +% Graph +\def\gA{{\mathcal{A}}} +\def\gB{{\mathcal{B}}} +\def\gC{{\mathcal{C}}} +\def\gD{{\mathcal{D}}} +\def\gE{{\mathcal{E}}} +\def\gF{{\mathcal{F}}} +\def\gG{{\mathcal{G}}} +\def\gH{{\mathcal{H}}} +\def\gI{{\mathcal{I}}} +\def\gJ{{\mathcal{J}}} +\def\gK{{\mathcal{K}}} +\def\gL{{\mathcal{L}}} +\def\gM{{\mathcal{M}}} +\def\gN{{\mathcal{N}}} +\def\gO{{\mathcal{O}}} +\def\gP{{\mathcal{P}}} +\def\gQ{{\mathcal{Q}}} +\def\gR{{\mathcal{R}}} +\def\gS{{\mathcal{S}}} +\def\gT{{\mathcal{T}}} +\def\gU{{\mathcal{U}}} +\def\gV{{\mathcal{V}}} +\def\gW{{\mathcal{W}}} +\def\gX{{\mathcal{X}}} +\def\gY{{\mathcal{Y}}} +\def\gZ{{\mathcal{Z}}} + +% Sets +\def\sA{{\mathbb{A}}} +\def\sB{{\mathbb{B}}} +\def\sC{{\mathbb{C}}} +\def\sD{{\mathbb{D}}} +% Don't use a set called E, because this would be the same as our symbol +% for expectation. +\def\sF{{\mathbb{F}}} +\def\sG{{\mathbb{G}}} +\def\sH{{\mathbb{H}}} +\def\sI{{\mathbb{I}}} +\def\sJ{{\mathbb{J}}} +\def\sK{{\mathbb{K}}} +\def\sL{{\mathbb{L}}} +\def\sM{{\mathbb{M}}} +\def\sN{{\mathbb{N}}} +\def\sO{{\mathbb{O}}} +\def\sP{{\mathbb{P}}} +\def\sQ{{\mathbb{Q}}} +\def\sR{{\mathbb{R}}} +\def\sS{{\mathbb{S}}} +\def\sT{{\mathbb{T}}} +\def\sU{{\mathbb{U}}} +\def\sV{{\mathbb{V}}} +\def\sW{{\mathbb{W}}} +\def\sX{{\mathbb{X}}} +\def\sY{{\mathbb{Y}}} +\def\sZ{{\mathbb{Z}}} + +% Entries of a matrix +\def\emLambda{{\Lambda}} +\def\emA{{A}} +\def\emB{{B}} +\def\emC{{C}} +\def\emD{{D}} +\def\emE{{E}} +\def\emF{{F}} +\def\emG{{G}} +\def\emH{{H}} +\def\emI{{I}} +\def\emJ{{J}} +\def\emK{{K}} +\def\emL{{L}} +\def\emM{{M}} +\def\emN{{N}} +\def\emO{{O}} +\def\emP{{P}} +\def\emQ{{Q}} +\def\emR{{R}} +\def\emS{{S}} +\def\emT{{T}} +\def\emU{{U}} +\def\emV{{V}} +\def\emW{{W}} +\def\emX{{X}} +\def\emY{{Y}} +\def\emZ{{Z}} +\def\emSigma{{\Sigma}} + +% entries of a tensor +% Same font as tensor, without \bm wrapper +\newcommand{\etens}[1]{\mathsfit{#1}} +\def\etLambda{{\etens{\Lambda}}} +\def\etA{{\etens{A}}} +\def\etB{{\etens{B}}} +\def\etC{{\etens{C}}} +\def\etD{{\etens{D}}} +\def\etE{{\etens{E}}} +\def\etF{{\etens{F}}} +\def\etG{{\etens{G}}} +\def\etH{{\etens{H}}} +\def\etI{{\etens{I}}} +\def\etJ{{\etens{J}}} +\def\etK{{\etens{K}}} +\def\etL{{\etens{L}}} +\def\etM{{\etens{M}}} +\def\etN{{\etens{N}}} +\def\etO{{\etens{O}}} +\def\etP{{\etens{P}}} +\def\etQ{{\etens{Q}}} +\def\etR{{\etens{R}}} +\def\etS{{\etens{S}}} +\def\etT{{\etens{T}}} +\def\etU{{\etens{U}}} +\def\etV{{\etens{V}}} +\def\etW{{\etens{W}}} +\def\etX{{\etens{X}}} +\def\etY{{\etens{Y}}} +\def\etZ{{\etens{Z}}} + +% The true underlying data generating distribution +\newcommand{\pdata}{p_{\rm{data}}} +% The empirical distribution defined by the training set +\newcommand{\ptrain}{\hat{p}_{\rm{data}}} +\newcommand{\Ptrain}{\hat{P}_{\rm{data}}} +% The model distribution +\newcommand{\pmodel}{p_{\rm{model}}} +\newcommand{\Pmodel}{P_{\rm{model}}} +\newcommand{\ptildemodel}{\tilde{p}_{\rm{model}}} +% Stochastic autoencoder distributions +\newcommand{\pencode}{p_{\rm{encoder}}} +\newcommand{\pdecode}{p_{\rm{decoder}}} +\newcommand{\precons}{p_{\rm{reconstruct}}} + +\newcommand{\laplace}{\mathrm{Laplace}} % Laplace distribution + +\newcommand{\E}{\mathbb{E}} +\newcommand{\Ls}{\mathcal{L}} +\newcommand{\R}{\mathbb{R}} +\newcommand{\emp}{\tilde{p}} +\newcommand{\lr}{\alpha} +\newcommand{\reg}{\lambda} +\newcommand{\rect}{\mathrm{rectifier}} +\newcommand{\softmax}{\mathrm{softmax}} +\newcommand{\sigmoid}{\sigma} +\newcommand{\softplus}{\zeta} +\newcommand{\KL}{D_{\mathrm{KL}}} +\newcommand{\Var}{\mathrm{Var}} +\newcommand{\standarderror}{\mathrm{SE}} +\newcommand{\Cov}{\mathrm{Cov}} +% Wolfram Mathworld says $L^2$ is for function spaces and $\ell^2$ is for vectors +% But then they seem to use $L^2$ for vectors throughout the site, and so does +% wikipedia. +\newcommand{\normlzero}{L^0} +\newcommand{\normlone}{L^1} +\newcommand{\normltwo}{L^2} +\newcommand{\normlp}{L^p} +\newcommand{\normmax}{L^\infty} + +\newcommand{\parents}{Pa} % See usage in notation.tex. 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b/docs/papers/2002.06100.pdf deleted file mode 100644 index aaaefe6..0000000 Binary files a/docs/papers/2002.06100.pdf and /dev/null differ diff --git a/docs/papers/PAYANI-DISSERTATION-2020.pdf b/docs/papers/PAYANI-DISSERTATION-2020.pdf deleted file mode 100644 index 8d27540..0000000 Binary files a/docs/papers/PAYANI-DISSERTATION-2020.pdf and /dev/null differ diff --git a/docs/papers/minimax-algebra.pdf b/docs/papers/minimax-algebra.pdf deleted file mode 100644 index 84fd0b6..0000000 Binary files a/docs/papers/minimax-algebra.pdf and /dev/null differ diff --git a/docs/proofs.nb b/docs/proofs.nb new file mode 100644 index 0000000..e04f481 --- /dev/null +++ b/docs/proofs.nb @@ -0,0 +1,72479 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 13.0' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] 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"Input",ExpressionUUID->"b0c721c2-75cf-45b3-9fdd-eddceb44ff5c"], +Cell[4085583, 72072, 524, 10, 60, "Output",ExpressionUUID->"1cca5d2b-5cae-41d7-aff9-55889d878555"] +}, Open ]] +}, Open ]] +}, Open ]] +} +] +*) + diff --git a/docs/toy-example-architecture.png b/docs/toy-example-architecture.png new file mode 100644 index 0000000..153876a Binary files /dev/null and b/docs/toy-example-architecture.png differ diff --git a/neurallogic/hard_and.py b/neurallogic/hard_and.py index 02d49d6..2dd7259 100644 --- a/neurallogic/hard_and.py +++ b/neurallogic/hard_and.py @@ -1,38 +1,42 @@ -from typing import Any +from typing import Callable import jax from flax import linen as nn -from typing import Callable - - -from neurallogic import neural_logic_net, symbolic_generation +from neurallogic import hard_masks, neural_logic_net, symbolic_generation, initialization -def soft_and_include(w: float, x: float) -> float: - """ - w > 0.5 implies the and operation is active, else inactive - - Assumes x is in [0, 1] - - Corresponding hard logic: x OR ! w - """ - w = jax.numpy.clip(w, 0.0, 1.0) - return jax.numpy.maximum(x, 1.0 - w) - - - -def hard_and_include(w, x): - return jax.numpy.logical_or(x, jax.numpy.logical_not(w)) +def soft_and(x, y): + m = jax.numpy.minimum(x, y) + return jax.numpy.where( + 2 * m > 1, + 0.5 + 0.5 * (x + y) * (m - 0.5), + m + 0.5 * (x + y) * (0.5 - m), + ) +def soft_and_vec(x): + m = jax.numpy.min(x) + mean = jax.numpy.mean(x) + delta = jax.numpy.abs(mean - 0.5) + return jax.numpy.where( + 2 * m > 1, + 0.5 + delta, + m + delta + ) +# TODO: seperate and operation from mask operation def soft_and_neuron(w, x): - x = jax.vmap(soft_and_include, 0, 0)(w, x) + x = jax.vmap(hard_masks.soft_mask_to_true_margin, 0, 0)(w, x) + #x = jax.vmap(hard_masks.soft_mask_to_true, 0, 0)(w, x) return jax.numpy.min(x) +# TODO: doesn't seem to work as well +def soft_and_neuron_deprecated(w, x): + x = jax.vmap(hard_masks.soft_mask_to_true_margin, 0, 0)(w, x) + return soft_and_vec(x) def hard_and_neuron(w, x): - x = jax.vmap(hard_and_include, 0, 0)(w, x) + x = jax.vmap(hard_masks.hard_mask_to_true, 0, 0)(w, x) return jax.lax.reduce(x, True, jax.lax.bitwise_and, [0]) @@ -41,18 +45,6 @@ def hard_and_neuron(w, x): hard_and_layer = jax.vmap(hard_and_neuron, (0, None), 0) -def initialize_near_to_zero(): - # TODO: investigate better initialization - def init(key, shape, dtype): - dtype = jax.dtypes.canonicalize_dtype(dtype) - # Sample from standard normal distribution (zero mean, unit variance) - x = jax.random.normal(key, shape, dtype) - # Transform to a normal distribution with mean -1 and standard deviation 0.5 - x = 0.5 * x - 1 - x = jax.numpy.clip(x, 0.001, 0.999) - return x - return init - class SoftAndLayer(nn.Module): """ @@ -62,15 +54,17 @@ class SoftAndLayer(nn.Module): layer_size: The number of neurons in the layer. weights_init: The initializer function for the weight matrix. """ + layer_size: int - weights_init: Callable = initialize_near_to_zero() + weights_init: Callable = initialization.initialize_near_to_zero() dtype: jax.numpy.dtype = jax.numpy.float32 @nn.compact def __call__(self, x): weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) - weights = self.param('bit_weights', self.weights_init, - weights_shape, self.dtype) + weights = self.param( + "bit_weights", self.weights_init, weights_shape, self.dtype + ) x = jax.numpy.asarray(x, self.dtype) return soft_and_layer(weights, x) @@ -83,13 +77,15 @@ class HardAndLayer(nn.Module): Attributes: layer_size: The number of neurons in the layer. """ + layer_size: int @nn.compact def __call__(self, x): weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) weights = self.param( - 'bit_weights', nn.initializers.constant(True), weights_shape) + "bit_weights", nn.initializers.constant(True), weights_shape + ) return hard_and_layer(weights, x) @@ -104,6 +100,13 @@ def __call__(self, x): and_layer = neural_logic_net.select( - lambda layer_size, weights_init=initialize_near_to_zero(), dtype=jax.numpy.float32: SoftAndLayer(layer_size, weights_init, dtype), - lambda layer_size, weights_init=nn.initializers.constant(True), dtype=jax.numpy.float32: HardAndLayer(layer_size), - lambda layer_size, weights_init=nn.initializers.constant(True), dtype=jax.numpy.float32: SymbolicAndLayer(layer_size)) + lambda layer_size, weights_init=initialization.initialize_near_to_zero(), dtype=jax.numpy.float32: SoftAndLayer( + layer_size, weights_init, dtype + ), + lambda layer_size, weights_init=nn.initializers.constant( + True + ), dtype=jax.numpy.float32: HardAndLayer(layer_size), + lambda layer_size, weights_init=nn.initializers.constant( + True + ), dtype=jax.numpy.float32: SymbolicAndLayer(layer_size), +) diff --git a/neurallogic/hard_concatenate.py b/neurallogic/hard_concatenate.py new file mode 100644 index 0000000..2a79ae3 --- /dev/null +++ b/neurallogic/hard_concatenate.py @@ -0,0 +1,46 @@ +import jax +from flax import linen as nn + +from neurallogic import neural_logic_net, symbolic_generation + + +def soft_concatenate(x, axis): + return jax.numpy.concatenate(x, axis) + + +def hard_concatenate(x, axis): + return soft_concatenate(x, axis) + + +class SoftConcatenate(nn.Module): + axis: int + @nn.compact + def __call__(self, x): + return soft_concatenate(x, self.axis) + + +class HardConcatenate(nn.Module): + axis: int + @nn.compact + def __call__(self, x): + return hard_concatenate(x, self.axis) + + +class SymbolicConcatenate: + def __init__(self, axis): + self.hard_concatenate = HardConcatenate(axis) + + def __call__(self, x): + jaxpr = symbolic_generation.make_symbolic_flax_jaxpr( + self.hard_concatenate, x + ) + return symbolic_generation.symbolic_expression(jaxpr, x) + + +concatenate = neural_logic_net.select( + lambda x, axis: SoftConcatenate(axis)(x), + lambda x, axis: HardConcatenate(axis)(x), + lambda x, axis: SymbolicConcatenate(axis)(x), +) + +# TODO: add tests \ No newline at end of file diff --git a/neurallogic/hard_count.py b/neurallogic/hard_count.py new file mode 100644 index 0000000..080dbad --- /dev/null +++ b/neurallogic/hard_count.py @@ -0,0 +1,96 @@ +import jax +from flax import linen as nn + +from neurallogic import neural_logic_net, symbolic_generation, hard_and + + +def low_to_high(x, y): + return hard_and.soft_and(1 - x, y) + +def soft_count(x: jax.numpy.array): + """ + Returns an array of soft-bits, of length |x|+1, and where only 1 soft-bit is high. + The index of the high soft-bit indicates the total quantity of low and high bits in the input array. + i.e. if index i is high, then there are i low bits + + E.g. if x = [0.1, 0.9, 0.2, 0.6, 0.4], then the output is y=[low, low, low, high, low, low] + y[3] is high, which indicates that + - 3 bits are low + - 2 bits are high + + E.g. if x = [0.0, 0.2, 0.3, 0.1, 0.4], then the output is y=[low, low, low, low, low, high] + y[5] is high, which indicates that + - 5 bits are low + - 0 bits are high + + E.g. if x = [0.9, 0.8, 0.7, 0.6, 0.5], then the output is y=[high, low, low, low, low, low] + y[0] is high, which indicates that + - 0 bits are low + - 5 bits are high + """ + sorted_x = jax.numpy.sort(x, axis=-1) + low = jax.numpy.array([0.0]) + high = jax.numpy.array([1.0]) + sorted_x = jax.numpy.concatenate([low, sorted_x, high]) + return jax.vmap(low_to_high)(sorted_x[:-1], sorted_x[1:]) + +def augmented_bit(mean, representative_bit) -> float: + margin = jax.numpy.abs(representative_bit - 0.5) + margin_delta = mean * margin + representative_bit = jax.numpy.where( + representative_bit > 0.5, + 0.5 + margin_delta, + representative_bit + margin_delta, + ) + return representative_bit + +# TODO: investigate +def soft_count_packed(x: jax.numpy.array): + mean = jax.numpy.mean(x, axis=-1) + sorted_x = jax.numpy.sort(x, axis=-1) + low = jax.numpy.array([0.0]) + high = jax.numpy.array([1.0]) + sorted_x = jax.numpy.concatenate([low, sorted_x, high]) + sorted_x = jax.vmap(low_to_high)(sorted_x[:-1], sorted_x[1:]) + return jax.vmap(lambda x: augmented_bit(mean, x))(sorted_x) + +def hard_count(x: jax.numpy.array): + # We simply count the number of low bits + num_low_bits = jax.numpy.sum(x <= 0.5, axis=-1) + return jax.nn.one_hot(num_low_bits, num_classes=x.shape[-1] + 1) + + +soft_count_layer = jax.vmap(soft_count, in_axes=0) + +hard_count_layer = jax.vmap(hard_count, in_axes=0) + + +class SoftCountLayer(nn.Module): + @nn.compact + def __call__(self, x): + return soft_count_layer(x) + + +class HardCountLayer(nn.Module): + @nn.compact + def __call__(self, x): + return hard_count_layer(x) + + +class SymbolicCountLayer: + def __init__(self): + self.hard_count_layer = HardCountLayer() + + def __call__(self, x): + jaxpr = symbolic_generation.make_symbolic_flax_jaxpr( + self.hard_count_layer, x + ) + return symbolic_generation.symbolic_expression(jaxpr, x) + + +count_layer = neural_logic_net.select( + lambda: SoftCountLayer(), + lambda: HardCountLayer(), + lambda: SymbolicCountLayer(), +) + diff --git a/neurallogic/hard_dropout.py b/neurallogic/hard_dropout.py new file mode 100644 index 0000000..3c20ccf --- /dev/null +++ b/neurallogic/hard_dropout.py @@ -0,0 +1,93 @@ +from typing import Optional, Sequence, Callable + +import jax +from flax import linen as nn +from jax import lax, random + +from neurallogic import neural_logic_net + + +class SoftHardDropout(nn.Module): + """Create a dropout layer suitable for dropping soft-bit values. + Adapted from flax/stochastic.py + + + Note: When using :meth:`Module.apply() `, make sure + to include an RNG seed named `'dropout'`. For example:: + + model.apply({'params': params}, inputs=inputs, train=True, rngs={'dropout': dropout_rng})` + + Attributes: + rate: the dropout probability. (_not_ the keep rate!) + broadcast_dims: dimensions that will share the same dropout mask + deterministic: if false the inputs are scaled by `1 / (1 - rate)` and + masked, whereas if true, no mask is applied and the inputs are returned + as is. + rng_collection: the rng collection name to use when requesting an rng key. + """ + + rate: float + broadcast_dims: Sequence[int] = () + deterministic: Optional[bool] = None + rng_collection: str = "dropout" + dtype: jax.numpy.dtype = jax.numpy.float32 + dropout_function: Callable = lambda x: jax.numpy.full_like(x, 0.0) + + @nn.compact + def __call__(self, inputs, deterministic: Optional[bool] = None): + """Applies a random dropout mask to the input. + + Args: + inputs: the inputs that should be randomly masked. + Masking means setting the input bits to 0.5. + deterministic: if false the inputs are masked, + whereas if true, no mask is applied and the inputs are returned + as is. + + Returns: + The masked inputs + """ + deterministic = nn.merge_param( + "deterministic", self.deterministic, deterministic + ) + + if (self.rate == 0.0) or deterministic: + return inputs + + # Prevent gradient NaNs in 1.0 edge-case. + if self.rate == 1.0: + return jax.numpy.zeros_like(inputs) + + keep_prob = 1.0 - self.rate + rng = self.make_rng(self.rng_collection) + broadcast_shape = list(inputs.shape) + for dim in self.broadcast_dims: + broadcast_shape[dim] = 1 + mask = random.bernoulli(rng, p=keep_prob, shape=broadcast_shape) + mask = jax.numpy.broadcast_to(mask, inputs.shape) + """ + masked_values = jax.numpy.full_like( + inputs, self.dropout_value, dtype=self.dtype + ) + """ + masked_values = jax.vmap(self.dropout_function)(inputs) + return lax.select(mask, inputs, masked_values) + + +class HardHardDropout(nn.Module): + @nn.compact + def __call__(self, inputs, deterministic: Optional[bool] = None): + return inputs + + +class SymbolicHardDropout(nn.Module): + @nn.compact + def __call__(self, inputs, deterministic: Optional[bool] = None): + return inputs + + +hard_dropout = neural_logic_net.select( + lambda **kwargs: SoftHardDropout(**kwargs), + lambda **kwargs: HardHardDropout(**kwargs), + lambda **kwargs: SymbolicHardDropout(**kwargs), +) diff --git a/neurallogic/hard_majority.py b/neurallogic/hard_majority.py index 7d91121..941523a 100644 --- a/neurallogic/hard_majority.py +++ b/neurallogic/hard_majority.py @@ -1,18 +1,33 @@ import jax +from flax import linen as nn -from neurallogic import neural_logic_net +from neurallogic import neural_logic_net, symbolic_generation def majority_index(input_size: int) -> int: return (input_size - 1) // 2 +# TODO: properly factor with/without margin versions -def soft_majority(x: jax.numpy.array) -> float: +def majority_bit(x: jax.numpy.array) -> float: index = majority_index(x.shape[-1]) sorted_x = jax.numpy.sort(x, axis=-1) return jax.numpy.take(sorted_x, index, axis=-1) +def soft_majority(x: jax.numpy.array) -> float: + m_bit = majority_bit(x) + margin = jax.numpy.abs(m_bit - 0.5) + mean = jax.numpy.mean(x, axis=-1) + margin_delta = mean * margin + representative_bit = jax.numpy.where( + m_bit > 0.5, + 0.5 + margin_delta, + m_bit + margin_delta, + ) + return representative_bit + + def hard_majority(x: jax.numpy.array) -> bool: threshold = x.shape[-1] - majority_index(x.shape[-1]) return jax.numpy.sum(x, axis=-1) >= threshold @@ -23,9 +38,44 @@ def hard_majority(x: jax.numpy.array) -> bool: hard_majority_layer = jax.vmap(hard_majority, in_axes=0) -def symbolic_majority_layer(x): - return hard_majority_layer(x) +class SoftMajorityLayer(nn.Module): + """ + A soft-bit MAJORITY layer than transforms its inputs along the last dimension. + + Attributes: + layer_size: The number of neurons in the layer. + weights_init: The initializer function for the weight matrix. + """ + + @nn.compact + def __call__(self, x): + return soft_majority_layer(x) + + +class HardMajorityLayer(nn.Module): + @nn.compact + def __call__(self, x): + return hard_majority_layer(x) + + +class SymbolicMajorityLayer: + def __init__(self): + self.hard_majority_layer = HardMajorityLayer() + + def __call__(self, x): + jaxpr = symbolic_generation.make_symbolic_flax_jaxpr( + self.hard_majority_layer, x + ) + return symbolic_generation.symbolic_expression(jaxpr, x) majority_layer = neural_logic_net.select( - soft_majority_layer, hard_majority_layer, symbolic_majority_layer) + lambda: SoftMajorityLayer(), + lambda: HardMajorityLayer(), + lambda: SymbolicMajorityLayer(), +) + +# TODO: construct a majority-k generalisation of the above +# where k is the number of high-soft bits required for a majority +# and where k is a soft-bit parameter. Requires constructing +# a piecewise-continuous function (as per notebook). diff --git a/neurallogic/hard_masks.py b/neurallogic/hard_masks.py new file mode 100644 index 0000000..744864c --- /dev/null +++ b/neurallogic/hard_masks.py @@ -0,0 +1,165 @@ +from typing import Callable + +import jax +from flax import linen as nn + +from neurallogic import neural_logic_net, symbolic_generation, hard_and, hard_or, initialization + +# TODO: properly factor with/without margin versions + + +def soft_mask_to_true(w: float, x: float): + """ + w > 0.5 implies the mask operation is inactive, else active + + Assumes x is in [0, 1] + + Corresponding hard logic: x OR ! w + """ + w = jax.numpy.clip(w, 0.0, 1.0) + return jax.numpy.maximum(x, 1.0 - w) + +# Superior on noisy XOR +def soft_mask_to_true_margin(w: float, x: float) -> float: + w = jax.numpy.clip(w, 0.0, 1.0) + return hard_or.soft_or(x, 1.0 - w) + + + +def hard_mask_to_true(w, x): + return jax.numpy.logical_or(x, jax.numpy.logical_not(w)) + + +soft_mask_to_true_neuron = jax.vmap(soft_mask_to_true, 0, 0) +soft_mask_to_true_margin_neuron = jax.vmap(soft_mask_to_true_margin, 0, 0) + +hard_mask_to_true_neuron = jax.vmap(hard_mask_to_true, 0, 0) + + +soft_mask_to_true_layer = jax.vmap(soft_mask_to_true_neuron, (0, None), 0) +soft_mask_to_true_margin_layer = jax.vmap(soft_mask_to_true_margin_neuron, (0, None), 0) + +hard_mask_to_true_layer = jax.vmap(hard_mask_to_true_neuron, (0, None), 0) + + +def soft_mask_to_false(w: float, x: float): + """ + w > 0.5 implies the mask is inactive, else active + + Assumes x is in [0, 1] + + Corresponding hard logic: b AND w + """ + w = jax.numpy.clip(w, 0.0, 1.0) + # TODO: what is this madness? + return 1.0 - jax.numpy.maximum(1.0 - x, 1.0 - w) + +# Superior on noisy XOR +def soft_mask_to_false_margin(w: float, x: float) -> float: + w = jax.numpy.clip(w, 0.0, 1.0) + return hard_and.soft_and(x, w) + + +def hard_mask_to_false(w, x): + return jax.numpy.logical_and(x, w) + + +soft_mask_to_false_neuron = jax.vmap(soft_mask_to_false, 0, 0) +soft_mask_to_false_margin_neuron = jax.vmap(soft_mask_to_false_margin, 0, 0) + +hard_mask_to_false_neuron = jax.vmap(hard_mask_to_false, 0, 0) + + +soft_mask_to_false_layer = jax.vmap(soft_mask_to_false_neuron, (0, None), 0) +soft_mask_to_false_margin_layer = jax.vmap(soft_mask_to_false_margin_neuron, (0, None), 0) + +hard_mask_to_false_layer = jax.vmap(hard_mask_to_false_neuron, (0, None), 0) + + +class SoftMaskLayer(nn.Module): + mask_layer_operation: Callable + layer_size: int + weights_init: Callable = nn.initializers.uniform(1.0) + dtype: jax.numpy.dtype = jax.numpy.float32 + + @nn.compact + def __call__(self, x): + weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) + weights = self.param( + "bit_weights", self.weights_init, weights_shape, self.dtype + ) + x = jax.numpy.asarray(x, self.dtype) + return self.mask_layer_operation(weights, x) + + +class HardMaskLayer(nn.Module): + mask_layer_operation: Callable + layer_size: int + weights_init: Callable = nn.initializers.constant(True) + + @nn.compact + def __call__(self, x): + weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) + weights = self.param("bit_weights", self.weights_init, weights_shape) + return self.mask_layer_operation(weights, x) + + +class SymbolicMaskLayer: + def __init__(self, mask_layer): + self.hard_mask_layer = mask_layer + + def __call__(self, x): + jaxpr = symbolic_generation.make_symbolic_flax_jaxpr(self.hard_mask_layer, x) + return symbolic_generation.symbolic_expression(jaxpr, x) + + +mask_to_true_layer = neural_logic_net.select( + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: SoftMaskLayer( + soft_mask_to_true_layer, layer_size, weights_init, dtype + ), + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: HardMaskLayer(hard_mask_to_true_layer, layer_size), + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: SymbolicMaskLayer( + HardMaskLayer(hard_mask_to_true_layer, layer_size) + ), +) + + +mask_to_true_margin_layer = neural_logic_net.select( + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: SoftMaskLayer( + soft_mask_to_true_margin_layer, layer_size, weights_init, dtype + ), + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: HardMaskLayer(hard_mask_to_true_layer, layer_size), + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: SymbolicMaskLayer( + HardMaskLayer(hard_mask_to_true_layer, layer_size) + ), +) + +mask_to_false_layer = neural_logic_net.select( + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: SoftMaskLayer( + soft_mask_to_false_layer, layer_size, weights_init, dtype + ), + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: HardMaskLayer(hard_mask_to_false_layer, layer_size), + lambda layer_size, weights_init=nn.initializers.uniform( + 1.0 + ), dtype=jax.numpy.float32: SymbolicMaskLayer( + HardMaskLayer(hard_mask_to_false_layer, layer_size) + ), +) + +# TODO: mask to false margin layer \ No newline at end of file diff --git a/neurallogic/hard_not.py b/neurallogic/hard_not.py index 7466e17..cd3ff31 100644 --- a/neurallogic/hard_not.py +++ b/neurallogic/hard_not.py @@ -3,10 +3,10 @@ import jax from flax import linen as nn -from neurallogic import neural_logic_net, symbolic_generation +from neurallogic import neural_logic_net, symbolic_generation, hard_and, hard_or, initialization -def soft_not(w: float, x: float) -> float: +def soft_not(w, x): """ w > 0.5 implies the not operation is inactive, else active @@ -17,9 +17,14 @@ def soft_not(w: float, x: float) -> float: w = jax.numpy.clip(w, 0.0, 1.0) return 1.0 - w + x * (2.0 * w - 1.0) +# TODO: split out function of parameter, and not operation, in order to simplify +def soft_not_deprecated(w: float, x: float) -> float: + w = jax.numpy.clip(w, 0.0, 1.0) + # (w && x) || (! w && ! x) + return hard_or.soft_or(hard_and.soft_and(w, x), hard_and.soft_and(1.0 - w, 1.0 - x)) + -def hard_not(w: bool, x: bool) -> bool: - # ~(x ^ w) +def hard_not(w: bool, x: bool): return jax.numpy.logical_not(jax.numpy.logical_xor(x, w)) @@ -35,13 +40,15 @@ def hard_not(w: bool, x: bool) -> bool: class SoftNotLayer(nn.Module): layer_size: int - weights_init: Callable = nn.initializers.uniform(1.0) + weights_init: Callable = initialization.initialize_uniform_range(0.49, 0.51) dtype: jax.numpy.dtype = jax.numpy.float32 @nn.compact def __call__(self, x): weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) - weights = self.param("bit_weights", self.weights_init, weights_shape, self.dtype) + weights = self.param( + "bit_weights", self.weights_init, weights_shape, self.dtype + ) x = jax.numpy.asarray(x, self.dtype) return soft_not_layer(weights, x) @@ -68,7 +75,7 @@ def __call__(self, x): not_layer = neural_logic_net.select( - lambda layer_size, weights_init=nn.initializers.uniform(1.0), dtype=jax.numpy.float32: SoftNotLayer(layer_size, weights_init, dtype), - lambda layer_size, weights_init=nn.initializers.uniform(1.0), dtype=jax.numpy.float32: HardNotLayer(layer_size), - lambda layer_size, weights_init=nn.initializers.uniform(1.0), dtype=jax.numpy.float32: SymbolicNotLayer(layer_size), + lambda layer_size, weights_init=initialization.initialize_uniform_range(0.49, 0.51), dtype=jax.numpy.float32: SoftNotLayer(layer_size, weights_init, dtype), + lambda layer_size, weights_init=initialization.initialize_uniform_range(0.49, 0.51), dtype=jax.numpy.float32: HardNotLayer(layer_size), + lambda layer_size, weights_init=initialization.initialize_uniform_range(0.49, 0.51), dtype=jax.numpy.float32: SymbolicNotLayer(layer_size), ) diff --git a/neurallogic/hard_or.py b/neurallogic/hard_or.py index 574644f..7aefdb0 100644 --- a/neurallogic/hard_or.py +++ b/neurallogic/hard_or.py @@ -3,32 +3,46 @@ import jax from flax import linen as nn -from neurallogic import neural_logic_net, symbolic_generation - - -def soft_or_include(w: float, x: float) -> float: - """ - w > 0.5 implies the and operation is active, else inactive - - Assumes x is in [0, 1] - - Corresponding hard logic: b AND w - """ - w = jax.numpy.clip(w, 0.0, 1.0) - return 1.0 - jax.numpy.maximum(1.0 - x, 1.0 - w) - - -def hard_or_include(w, x): - return jax.numpy.logical_and(x, w) - - +from neurallogic import ( + neural_logic_net, + symbolic_generation, + hard_masks, + initialization, +) + + +def soft_or(x, y): + m = jax.numpy.maximum(x, y) + return jax.numpy.where( + 2 * m > 1, + 0.5 + 0.5 * (x + y) * (m - 0.5), + m + 0.5 * (x + y) * (0.5 - m), + ) + +def soft_or_vec(x): + m = jax.numpy.max(x) + mean = jax.numpy.mean(x) + delta = jax.numpy.abs(mean - 0.5) + return jax.numpy.where( + 2 * m > 1, + 0.5 + delta, + m + delta + ) + + +# TODO: seperate out the or operation from the mask operation def soft_or_neuron(w, x): - x = jax.vmap(soft_or_include, 0, 0)(w, x) + x = jax.vmap(hard_masks.soft_mask_to_false_margin, 0, 0)(w, x) return jax.numpy.max(x) +# TODO: doesn't seem to work as well +def soft_or_neuron_deprecated(w, x): + x = jax.vmap(hard_masks.soft_mask_to_false_margin, 0, 0)(w, x) + return soft_or_vec(x) + def hard_or_neuron(w, x): - x = jax.vmap(hard_or_include, 0, 0)(w, x) + x = jax.vmap(hard_masks.hard_mask_to_false, 0, 0)(w, x) return jax.lax.reduce(x, False, jax.lax.bitwise_or, [0]) @@ -36,31 +50,18 @@ def hard_or_neuron(w, x): hard_or_layer = jax.vmap(hard_or_neuron, (0, None), 0) -# TODO: investigate better initialization - - -def initialize_near_to_one(): - def init(key, shape, dtype): - dtype = jax.dtypes.canonicalize_dtype(dtype) - # Sample from standard normal distribution (zero mean, unit variance) - x = jax.random.normal(key, shape, dtype) - # Transform to a normal distribution with mean 1 and standard deviation 0.5 - x = 0.5 * x + 1 - x = jax.numpy.clip(x, 0.001, 0.999) - return x - return init - class SoftOrLayer(nn.Module): layer_size: int - weights_init: Callable = initialize_near_to_one() + weights_init: Callable = initialization.initialize_near_to_one() dtype: jax.numpy.dtype = jax.numpy.float32 @nn.compact def __call__(self, x): weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) weights = self.param( - 'bit_weights', self.weights_init, weights_shape, self.dtype) + "bit_weights", self.weights_init, weights_shape, self.dtype + ) x = jax.numpy.asarray(x, self.dtype) return soft_or_layer(weights, x) @@ -72,7 +73,8 @@ class HardOrLayer(nn.Module): def __call__(self, x): weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) weights = self.param( - 'bit_weights', nn.initializers.constant(True), weights_shape) + "bit_weights", nn.initializers.constant(True), weights_shape + ) return hard_or_layer(weights, x) @@ -82,14 +84,18 @@ def __init__(self, layer_size): self.hard_or_layer = HardOrLayer(self.layer_size) def __call__(self, x): - jaxpr = symbolic_generation.make_symbolic_flax_jaxpr( - self.hard_or_layer, x) + jaxpr = symbolic_generation.make_symbolic_flax_jaxpr(self.hard_or_layer, x) return symbolic_generation.symbolic_expression(jaxpr, x) or_layer = neural_logic_net.select( - lambda layer_size, weights_init=initialize_near_to_one( - ), dtype=jax.numpy.float32: SoftOrLayer(layer_size, weights_init, dtype), + lambda layer_size, weights_init=initialization.initialize_near_to_one(), dtype=jax.numpy.float32: SoftOrLayer( + layer_size, weights_init, dtype + ), + lambda layer_size, weights_init=nn.initializers.constant( + True + ), dtype=jax.numpy.float32: HardOrLayer(layer_size), lambda layer_size, weights_init=nn.initializers.constant( - True), dtype=jax.numpy.float32: HardOrLayer(layer_size), - lambda layer_size, weights_init=nn.initializers.constant(True), dtype=jax.numpy.float32: SymbolicOrLayer(layer_size)) + True + ), dtype=jax.numpy.float32: SymbolicOrLayer(layer_size), +) diff --git a/neurallogic/hard_vmap.py b/neurallogic/hard_vmap.py new file mode 100644 index 0000000..5e164fe --- /dev/null +++ b/neurallogic/hard_vmap.py @@ -0,0 +1,24 @@ +import jax +import numpy + +from neurallogic import neural_logic_net + + +def soft_vmap(f): + return jax.vmap(f) + + +def hard_vmap(f): + return soft_vmap(f) + + +def symbolic_vmap(f): + return numpy.vectorize(f, otypes=[object]) + +vmap = neural_logic_net.select( + lambda f: soft_vmap(f[0]), + lambda f: hard_vmap(f[1]), + lambda f: symbolic_vmap(f[2]) +) + +# TODO: add tests diff --git a/neurallogic/hard_xor.py b/neurallogic/hard_xor.py index 2a8ab30..9c75815 100644 --- a/neurallogic/hard_xor.py +++ b/neurallogic/hard_xor.py @@ -3,56 +3,45 @@ import jax from flax import linen as nn -from neurallogic import neural_logic_net, symbolic_generation +from neurallogic import neural_logic_net, symbolic_generation, hard_masks -def soft_xor_include(w: float, x: float) -> float: - """ - w > 0.5 implies the and operation is active, else inactive - - Assumes x is in [0, 1] - - Corresponding hard logic: b AND w - """ - w = jax.numpy.clip(w, 0.0, 1.0) - return 1.0 - jax.numpy.maximum(1.0 - x, 1.0 - w) - - -def hard_xor_include(w, x): - return jax.numpy.logical_and(x, w) +def differentiable_xor(x, y): + return jax.numpy.minimum(jax.numpy.maximum(x, y), 1.0 - jax.numpy.minimum(x, y)) +# TODO: seperate out the mask from the xor operation def soft_xor_neuron(w, x): # Conditionally include input bits, according to weights - x = jax.vmap(soft_xor_include, 0, 0)(w, x) - - def xor(x, y): - return jax.numpy.minimum(jax.numpy.maximum(x, y), 1.0 - jax.numpy.minimum(x, y)) - x = jax.lax.reduce(x, jax.numpy.float16(0.0), xor, (0,)) + x = jax.vmap(hard_masks.soft_mask_to_false, 0, 0)(w, x) + x = jax.lax.reduce(x, jax.numpy.array(0, dtype=x.dtype), differentiable_xor, (0,)) return x def hard_xor_neuron(w, x): - x = jax.vmap(hard_xor_include, 0, 0)(w, x) + x = jax.vmap(hard_masks.hard_mask_to_false, 0, 0)(w, x) return jax.lax.reduce(x, False, jax.lax.bitwise_xor, [0]) soft_xor_layer = jax.vmap(soft_xor_neuron, (0, None), 0) + hard_xor_layer = jax.vmap(hard_xor_neuron, (0, None), 0) class SoftXorLayer(nn.Module): layer_size: int - weights_init: Callable = nn.initializers.uniform( - 1.0) # TODO: investigate better initialization + weights_init: Callable = ( + nn.initializers.uniform(1.0) + ) dtype: jax.numpy.dtype = jax.numpy.float32 @nn.compact def __call__(self, x): weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) weights = self.param( - 'bit_weights', self.weights_init, weights_shape, self.dtype) + "bit_weights", self.weights_init, weights_shape, self.dtype + ) x = jax.numpy.asarray(x, self.dtype) return soft_xor_layer(weights, x) @@ -64,7 +53,8 @@ class HardXorLayer(nn.Module): def __call__(self, x): weights_shape = (self.layer_size, jax.numpy.shape(x)[-1]) weights = self.param( - 'bit_weights', nn.initializers.constant(True), weights_shape) + "bit_weights", nn.initializers.constant(True), weights_shape + ) return hard_xor_layer(weights, x) @@ -74,14 +64,18 @@ def __init__(self, layer_size): self.hard_xor_layer = HardXorLayer(self.layer_size) def __call__(self, x): - jaxpr = symbolic_generation.make_symbolic_flax_jaxpr( - self.hard_xor_layer, x) + jaxpr = symbolic_generation.make_symbolic_flax_jaxpr(self.hard_xor_layer, x) return symbolic_generation.symbolic_expression(jaxpr, x) xor_layer = neural_logic_net.select( lambda layer_size, weights_init=nn.initializers.uniform( - 1.0), dtype=jax.numpy.float32: SoftXorLayer(layer_size, weights_init, dtype), + 1.0 + ), dtype=jax.numpy.float32: SoftXorLayer(layer_size, weights_init, dtype), + lambda layer_size, weights_init=nn.initializers.constant( + True + ), dtype=jax.numpy.float32: HardXorLayer(layer_size), lambda layer_size, weights_init=nn.initializers.constant( - True), dtype=jax.numpy.float32: HardXorLayer(layer_size), - lambda layer_size, weights_init=nn.initializers.constant(True), dtype=jax.numpy.float32: SymbolicXorLayer(layer_size)) + True + ), dtype=jax.numpy.float32: SymbolicXorLayer(layer_size), +) diff --git a/neurallogic/harden.py b/neurallogic/harden.py index 099fbf2..e25f5d8 100644 --- a/neurallogic/harden.py +++ b/neurallogic/harden.py @@ -62,13 +62,6 @@ def harden(x: flax.core.FrozenDict): return harden(x.unfreeze()) -@dispatch -def harden(*args): - if len(args) == 1: - return harden(args[0]) - return tuple([harden(arg) for arg in args]) - - @dispatch def map_keys_nested(f, d: dict) -> dict: return { diff --git a/neurallogic/harden_layer.py b/neurallogic/harden_layer.py index a2d6665..255d93a 100644 --- a/neurallogic/harden_layer.py +++ b/neurallogic/harden_layer.py @@ -3,25 +3,40 @@ from neurallogic import neural_logic_net -def harden_element(x): +def logistic_clip(x): + return jax.scipy.special.expit(3 * (2 * x - 1)) + + +def harden(x): # non-differentiable return jax.lax.cond(x > 0.5, lambda _: 1.0, lambda _: 0.0, None) -def straight_through_harden_element(x): - # Create an exactly-zero expression with Sterbenz lemma that has - # an exactly-one gradient. - zero = x - jax.lax.stop_gradient(x) - return zero + jax.lax.stop_gradient(harden_element(x)) -soft_harden_layer = jax.vmap(straight_through_harden_element) +def straight_through_harden(x): + # The harden operation is non-differentiable. Therefore we need to + # approximate with the straight-through estimator. + + # Create an exactly-zero expression with Sterbenz lemma that has + # an exactly-one gradient. + zero = x - jax.lax.stop_gradient(x) + grad_of_one = zero + jax.lax.stop_gradient(harden(x)) + return grad_of_one + + +soft_harden_layer = jax.vmap(straight_through_harden) + def hard_harden_layer(x): return x -#TODO: can we harden arbitrary tensors? -#TODO: is this correct? + +# TODO: can we harden arbitrary tensors? +# TODO: is this correct? def symbolic_harden_layer(x): return x -harden_layer = neural_logic_net.select(soft_harden_layer, hard_harden_layer, symbolic_harden_layer) +harden_layer = neural_logic_net.select( + soft_harden_layer, hard_harden_layer, symbolic_harden_layer +) + \ No newline at end of file diff --git a/neurallogic/initialization.py b/neurallogic/initialization.py new file mode 100644 index 0000000..d31ea9c --- /dev/null +++ b/neurallogic/initialization.py @@ -0,0 +1,58 @@ +import jax + + +def initialize_uniform_range(lower=0.0, upper=1.0): + def init(key, shape, dtype): + dtype = jax.dtypes.canonicalize_dtype(dtype) + x = jax.random.uniform(key, shape, dtype, lower, upper) + return x + + return init + + +def initialize_near_to_zero(mean=-1, std=0.5): + def init(key, shape, dtype): + dtype = jax.dtypes.canonicalize_dtype(dtype) + # Sample from standard normal distribution (zero mean, unit variance) + x = jax.random.normal(key, shape, dtype) + # Transform to a normal distribution with mean -1 and standard deviation 0.5 + x = std * x + mean + x = jax.numpy.clip(x, 0.001, 0.999) + return x + + return init + + +def initialize_near_to_one(): + def init(key, shape, dtype): + dtype = jax.dtypes.canonicalize_dtype(dtype) + # Sample from standard normal distribution (zero mean, unit variance) + x = jax.random.normal(key, shape, dtype) + # Transform to a normal distribution with mean 1 and standard deviation 0.5 + x = 0.5 * x + 1 + x = jax.numpy.clip(x, 0.001, 0.999) + return x + + return init + + +# TODO: get rid of symmetry +def initialize_bernoulli(p=0.5, low=0.001, high=0.999): + def init(key, shape, dtype): + x = jax.random.bernoulli(key, p, shape) + x = jax.numpy.where(x, high, low) + x = jax.numpy.asarray(x, dtype) + return x + + return init + +def initialize_bernoulli_uniform(p=0.5, low=0.001, high=0.999): + def init(key, shape, dtype): + x = jax.random.bernoulli(key, p, shape) + h = jax.random.uniform(key, shape, dtype, 0.5, high) + l = jax.random.uniform(key, shape, dtype, low, 0.5) + x = jax.numpy.where(x, h, l) + x = jax.numpy.asarray(x, dtype) + return x + + return init diff --git a/neurallogic/map_at_elements.py b/neurallogic/map_at_elements.py index f4698df..9a81450 100644 --- a/neurallogic/map_at_elements.py +++ b/neurallogic/map_at_elements.py @@ -30,6 +30,11 @@ def map_at_elements(x: numpy.float32, func: typing.Callable): return func(x) +@dispatch +def map_at_elements(x: numpy.int32, func: typing.Callable): + return func(x) + + @dispatch def map_at_elements(x: list, func: typing.Callable): return [map_at_elements(item, func) for item in x] @@ -55,4 +60,3 @@ def map_at_elements(x: dict, func: typing.Callable): @dispatch def map_at_elements(x: tuple, func: typing.Callable): return tuple(map_at_elements(list(x), func)) - diff --git a/neurallogic/neural_logic_net.py b/neurallogic/neural_logic_net.py index e74f92c..4f65489 100644 --- a/neurallogic/neural_logic_net.py +++ b/neurallogic/neural_logic_net.py @@ -1,29 +1,32 @@ from enum import Enum from flax import linen as nn -NetType = Enum('NetType', ['Soft', 'Hard', 'Symbolic']) +NetType = Enum("NetType", ["Soft", "Hard", "Symbolic"]) + def select(soft, hard, symbolic): def selector(type: NetType): - return { - NetType.Soft: soft, - NetType.Hard: hard, - NetType.Symbolic: symbolic - }[type] + return {NetType.Soft: soft, NetType.Hard: hard, NetType.Symbolic: symbolic}[ + type + ] + return selector + def net(f): class SoftNet(nn.Module): @nn.compact - def __call__(self, x): - return f(NetType.Soft, x) - class HardNet(nn.Module): + def __call__(self, x, **kwargs): + return f(NetType.Soft, x, **kwargs) + + class HardNet(nn.Module): @nn.compact - def __call__(self, x): - return f(NetType.Hard, x) + def __call__(self, x, **kwargs): + return f(NetType.Hard, x, **kwargs) + class SymbolicNet(nn.Module): @nn.compact - def __call__(self, x): - return f(NetType.Symbolic, x) - return SoftNet(), HardNet(), SymbolicNet() + def __call__(self, x, **kwargs): + return f(NetType.Symbolic, x, **kwargs) + return SoftNet(), HardNet(), SymbolicNet() diff --git a/neurallogic/real_encoder.py b/neurallogic/real_encoder.py index 8ec422b..1613f4c 100644 --- a/neurallogic/real_encoder.py +++ b/neurallogic/real_encoder.py @@ -5,27 +5,27 @@ from neurallogic import neural_logic_net, symbolic_generation -# TODO: perhaps this can be simplified with a simple multiplication? # TODO: implement a soft_real_decoder that can perhaps replace the port count approach -def soft_real_encoder(t: float, x: float) -> float: + +def soft_real_encoder(t: float, x: float): eps = 0.0000001 # x should be in [0, 1] - t = jax.numpy.clip(t, 0.0, 1.0) + t = jax.numpy.clip(t, 0, 1) return jax.numpy.where( jax.numpy.isclose(t, x), 0.5, # t != x jax.numpy.where( x < t, - (1.0 / (2.0 * t + eps)) * x, + (x / (2 * t + eps)), # x > t - (1.0 / (2.0 * (1.0 - t) + eps)) * (x + 1.0 - 2.0 * t) + (x + 1 - 2 * t) / (2 * (1 - t) + eps) ) ) -def hard_real_encoder(t: float, x: float) -> bool: +def hard_real_encoder(t, x): # t and x must be floats return jax.numpy.where(soft_real_encoder(t, x) > 0.5, True, False) diff --git a/neurallogic/symbolic_generation.py b/neurallogic/symbolic_generation.py index 4b4440c..9e974f2 100644 --- a/neurallogic/symbolic_generation.py +++ b/neurallogic/symbolic_generation.py @@ -14,9 +14,9 @@ def symbolic_bind(prim, *args, **params): -# print('\nprimitive: ', prim.name) -# print('\targs:\n\t\t', args) -# print('\tparams\n\t\t: ', params) + #print('\nprimitive: ', prim.name) + #print('\targs:\n\t\t', args) + #print('\tparams\n\t\t: ', params) symbolic_outvals = { 'broadcast_in_dim': symbolic_primitives.symbolic_broadcast_in_dim, 'reshape': symbolic_primitives.symbolic_reshape, @@ -28,13 +28,17 @@ def symbolic_bind(prim, *args, **params): 'lt': symbolic_primitives.symbolic_lt, 'ge': symbolic_primitives.symbolic_ge, 'gt': symbolic_primitives.symbolic_gt, - 'abs': symbolic_primitives.symbolic_abs, 'add': symbolic_primitives.symbolic_add, 'sub': symbolic_primitives.symbolic_sub, 'mul': symbolic_primitives.symbolic_mul, 'div': symbolic_primitives.symbolic_div, + 'tan': symbolic_primitives.symbolic_tan, 'max': symbolic_primitives.symbolic_max, 'min': symbolic_primitives.symbolic_min, + 'abs': symbolic_primitives.symbolic_abs, + 'round': symbolic_primitives.symbolic_round, + 'floor': symbolic_primitives.symbolic_floor, + 'ceil': symbolic_primitives.symbolic_ceil, 'and': symbolic_primitives.symbolic_and, 'or': symbolic_primitives.symbolic_or, 'xor': symbolic_primitives.symbolic_xor, @@ -93,13 +97,15 @@ def make_symbolic_flax_jaxpr(flax_layer, x): x = numpy.asarray(x, dtype=numpy.int32) # Make the jaxpr that corresponds to the flax layer jaxpr = make_symbolic_jaxpr(flax_layer, x) - # Make a list of bit_weights and thresholds but only include each if they are not None - bit_weights_and_thresholds = [x for x in [bit_weights, thresholds] if x is not None] - # Replace the dummy numeric weights with the actual weights in the jaxpr - jaxpr.consts = bit_weights_and_thresholds + if hasattr(jaxpr, '_consts'): + # Make a list of bit_weights and thresholds but only include each if they are not None + bit_weights_and_thresholds = [x for x in [bit_weights, thresholds] if x is not None] + # Replace the dummy numeric weights with the actual weights in the jaxpr + jaxpr.__setattr__('_consts', bit_weights_and_thresholds) return jaxpr + def eval_jaxpr(symbolic, jaxpr, consts, *args): '''Evaluates a jaxpr by interpreting it as Python code. @@ -189,10 +195,9 @@ def eval_jaxpr_impl(jaxpr): outvals = [outvals] symbolic_outvals = [symbolic_outvals] if not symbolic: - # Check that the concrete and symbolic values are equal - # print( - # f'outvals: {outvals} and symbolic_outvals: {symbolic_outvals}' - # ) + # Always check that the symbolic binding generates the same values as the + # standard jax binding in order to detect bugs early. + # print(f'outvals: {outvals} and symbolic_outvals: {symbolic_outvals}') assert numpy.allclose( numpy.array(outvals), symbolic_outvals, equal_nan=True ) @@ -212,15 +217,15 @@ def eval_jaxpr_impl(jaxpr): def make_symbolic_jaxpr(func: typing.Callable, *args): return jax.make_jaxpr(lambda *args: func(*args))(*args) - -def eval_symbolic(symbolic_function, *args): - if hasattr(symbolic_function, 'literals'): +# TODO: better name +def eval_symbolic(jaxpr, *args): + if hasattr(jaxpr, 'literals'): return eval_jaxpr( - False, symbolic_function.jaxpr, symbolic_function.literals, *args + False, jaxpr.jaxpr, jaxpr.literals, *args ) - return eval_jaxpr(False, symbolic_function.jaxpr, [], *args) - + return eval_jaxpr(False, jaxpr.jaxpr, [], *args) +# TODO: better name def symbolic_expression(jaxpr, *args): if hasattr(jaxpr, 'literals'): sym_expr = eval_jaxpr(True, jaxpr.jaxpr, jaxpr.literals, *args) diff --git a/neurallogic/symbolic_operator.py b/neurallogic/symbolic_operator.py index 9960004..54c7694 100644 --- a/neurallogic/symbolic_operator.py +++ b/neurallogic/symbolic_operator.py @@ -8,11 +8,21 @@ def symbolic_operator(operator: str, x: str) -> str: return f'{operator}({x})'.replace('\'', '') +@dispatch +def symbolic_operator(operator: str, x: str, y: str): + return f'{operator}({x}, {y})'.replace('\'', '') + + @dispatch def symbolic_operator(operator: str, x: float, y: str): return symbolic_operator(operator, str(x), y) +@dispatch +def symbolic_operator(operator: str, x: int, y: str): + return symbolic_operator(operator, str(x), y) + + @dispatch def symbolic_operator(operator: str, x: str, y: float): return symbolic_operator(operator, x, str(y)) @@ -28,11 +38,6 @@ def symbolic_operator(operator: str, x: numpy.ndarray, y: numpy.ndarray): return numpy.vectorize(symbolic_operator, otypes=[object])(operator, x, y) -@dispatch -def symbolic_operator(operator: str, x: str, y: str): - return f'{operator}({x}, {y})'.replace('\'', '') - - @dispatch def symbolic_operator(operator: str, x: numpy.ndarray, y: float): return numpy.vectorize(symbolic_operator, otypes=[object])(operator, x, y) @@ -63,6 +68,11 @@ def symbolic_operator(operator: str, x: str, y: int): return symbolic_operator(operator, x, str(y)) +@dispatch +def symbolic_operator(operator: str, x: tuple): + return symbolic_operator(operator, str(x)) + + @dispatch def symbolic_operator(operator: str, x: list, y: numpy.ndarray): return numpy.vectorize(symbolic_operator, otypes=[object])(operator, x, y) @@ -81,4 +91,3 @@ def symbolic_operator(operator: str, x: numpy.ndarray): @dispatch def symbolic_operator(operator: str, x: list): return symbolic_operator(operator, numpy.array(x)) - diff --git a/neurallogic/symbolic_primitives.py b/neurallogic/symbolic_primitives.py index 47d08f4..0d2a79a 100644 --- a/neurallogic/symbolic_primitives.py +++ b/neurallogic/symbolic_primitives.py @@ -1,5 +1,8 @@ +from typing import Callable + import jax import jax._src.lax_reference as lax_reference +import jax._src.lax.lax as lax import numpy from neurallogic import symbolic_operator, symbolic_representation @@ -19,152 +22,109 @@ def all_concrete_values(data): return True -def symbolic_not(*args, **kwargs): +def symbolic(concrete_function: Callable, symbolic_function: str, *args, **kwargs): if all_concrete_values([*args]): - return numpy.logical_not(*args, **kwargs) + # We can directly evaluate the function + return concrete_function(*args, **kwargs) else: - return symbolic_operator.symbolic_operator('numpy.logical_not', *args, **kwargs) + # We need to return a symbolic representation + return symbolic_operator.symbolic_operator(symbolic_function, *args, **kwargs) + + +def symbolic_not(*args, **kwargs): + return symbolic(numpy.logical_not, 'numpy.logical_not', *args, **kwargs) def symbolic_eq(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.eq(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.eq', *args, **kwargs) + return symbolic(lax_reference.eq, 'lax_reference.eq', *args, **kwargs) def symbolic_ne(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.ne(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.ne', *args, **kwargs) + return symbolic(lax_reference.ne, 'lax_reference.ne', *args, **kwargs) def symbolic_le(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.le(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.le', *args, **kwargs) + return symbolic(lax_reference.le, 'lax_reference.le', *args, **kwargs) def symbolic_lt(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.lt(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.lt', *args, **kwargs) + return symbolic(lax_reference.lt, 'lax_reference.lt', *args, **kwargs) def symbolic_ge(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.ge(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.ge', *args, **kwargs) + return symbolic(lax_reference.ge, 'lax_reference.ge', *args, **kwargs) def symbolic_gt(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.gt(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.gt', *args, **kwargs) + return symbolic(lax_reference.gt, 'lax_reference.gt', *args, **kwargs) def symbolic_abs(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.abs(*args, **kwargs) + return symbolic(lax_reference.abs, 'lax_reference.abs', *args, **kwargs) + + +def symbolic_floor(*args, **kwargs): + return symbolic(lax_reference.floor, 'lax_reference.floor', *args, **kwargs) + + +def symbolic_ceil(*args, **kwargs): + return symbolic(lax_reference.ceil, 'lax_reference.ceil', *args, **kwargs) + + +def symbolic_round(*args, **kwargs): + # The reference implementation only supports away from zero + if kwargs['rounding_method'] == lax.RoundingMethod.AWAY_FROM_ZERO: + return symbolic(lax_reference.round, 'lax_reference.round', *args) + elif kwargs['rounding_method'] == lax.RoundingMethod.TO_NEAREST_EVEN: + return symbolic(numpy.around, 'numpy.around', *args) else: - return symbolic_operator.symbolic_operator('numpy.absolute', *args, **kwargs) + raise NotImplementedError( + f'rounding_method {str(kwargs["rounding_method"])} not implemented') def symbolic_add(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.add(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('numpy.add', *args, **kwargs) + return symbolic(lax_reference.add, 'lax_reference.add', *args, **kwargs) def symbolic_sub(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.sub(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('numpy.subtract', *args, **kwargs) + return symbolic(lax_reference.sub, 'lax_reference.sub', *args, **kwargs) def symbolic_mul(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.mul(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('numpy.multiply', *args, **kwargs) + return symbolic(lax_reference.mul, 'lax_reference.mul', *args, **kwargs) def symbolic_div(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.div(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.div', *args, **kwargs) + return symbolic(lax_reference.div, 'lax_reference.div', *args, **kwargs) -def symbolic_max(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.max(*args, **kwargs) - else: - r = symbolic_operator.symbolic_operator('numpy.maximum', *args, **kwargs) - return r +def symbolic_tan(*args, **kwargs): + return symbolic(lax_reference.tan, 'lax_reference.tan', *args, **kwargs) -def symbolic_min(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.min(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('numpy.minimum', *args, **kwargs) +def symbolic_max(*args, **kwargs): + return symbolic(lax_reference.max, 'lax_reference.max', *args, **kwargs) -def symbolic_select_n(*args, **kwargs): - ''' - Important comment from lax.py - # Caution! The select_n_p primitive has the *opposite* order of arguments to - # select(). This is because it implements `select_n`. - ''' - pred = args[0] - on_true = args[1] - on_false = args[2] - if all_concrete_values([*args]): - # swap order of on_true and on_false - return lax_reference.select(pred, on_false, on_true) - else: - # swap order of on_true and on_false - # TODO: need a more general solution to unquoting symbolic strings - evaluable_pred = symbolic_representation.symbolic_representation(pred) - evaluable_on_true = symbolic_representation.symbolic_representation(on_true) - evaluable_on_false = symbolic_representation.symbolic_representation(on_false) - return f'lax_reference.select({evaluable_pred}, {evaluable_on_false}, {evaluable_on_true})' +def symbolic_min(*args, **kwargs): + return symbolic(lax_reference.min, 'lax_reference.min', *args, **kwargs) def symbolic_and(*args, **kwargs): - if all_concrete_values([*args]): - return numpy.logical_and(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('numpy.logical_and', *args, **kwargs) + return symbolic(numpy.logical_and, 'numpy.logical_and', *args, **kwargs) def symbolic_or(*args, **kwargs): - if all_concrete_values([*args]): - return numpy.logical_or(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('numpy.logical_or', *args, **kwargs) + return symbolic(numpy.logical_or, 'numpy.logical_or', *args, **kwargs) def symbolic_xor(*args, **kwargs): - if all_concrete_values([*args]): - return numpy.logical_xor(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('numpy.logical_xor', *args, **kwargs) + return symbolic(numpy.logical_xor, 'numpy.logical_xor', *args, **kwargs) def symbolic_sum(*args, **kwargs): - if all_concrete_values([*args]): - return lax_reference.sum(*args, **kwargs) - else: - return symbolic_operator.symbolic_operator('lax_reference.sum', *args, **kwargs) + # N.B. We pass the tuple directly because we're summing over all args + return symbolic(lax_reference.sum, 'lax_reference.sum', args, **kwargs) def symbolic_broadcast_in_dim(*args, **kwargs): @@ -194,6 +154,32 @@ def convert_element_type(x, dtype): return convert_element_type(*args, dtype=kwargs['new_dtype']) +def symbolic_select_n(*args, **kwargs): + ''' + Important comment from lax.py + # Caution! The select_n_p primitive has the *opposite* order of arguments to + # select(). This is because it implements `select_n`. + ''' + pred = args[0] + on_true = args[1] + on_false = args[2] + if all_concrete_values([*args]): + # swap order of on_true and on_false + return lax_reference.select(pred, on_false, on_true) + else: + # TODO: to retain tensor structure we need to push down the select to the + # lowest level of the symbolic expression tree. This is not currently + # implemented. + print('WARNING: symbolic_select_n is not fully implemented. This may not work as expected.') + # swap order of on_true and on_false + evaluable_pred = symbolic_representation.symbolic_representation(pred) + evaluable_on_true = symbolic_representation.symbolic_representation( + on_true) + evaluable_on_false = symbolic_representation.symbolic_representation( + on_false) + return f'lax_reference.select({evaluable_pred}, {evaluable_on_false}, {evaluable_on_true})' + + def make_symbolic_reducer(py_binop, init_val): # This function is a hack to get around the fact that JAX doesn't # support symbolic reduction operations. It takes a symbolic reduction diff --git a/neurallogic/symbolic_representation.py b/neurallogic/symbolic_representation.py index 35595b2..98b09c1 100644 --- a/neurallogic/symbolic_representation.py +++ b/neurallogic/symbolic_representation.py @@ -1,6 +1,7 @@ import numpy from plum import dispatch +# TODO: need a more general solution to unquoting symbolic strings @dispatch def symbolic_representation(x: numpy.ndarray): diff --git a/prototype/neural-logic.m b/prototype/neural-logic.m index b655efc..0569d96 100644 --- a/prototype/neural-logic.m +++ b/prototype/neural-logic.m @@ -361,6 +361,12 @@ an association (rather than consuming nested lists). This would avoid problems DifferentiableHardAND[b_, w_] := If[w > 1/2, If[b > 1/2, b, (2w -1)b + 1 - w], If[b > 1/2, -2w(1 - b) + 1, 1 - w]] *) +(* For Wolfram Tech conference demo *) +(* +DifferentiableHardAND[b_, w_] := If[Min[b, w] > 1/2, 1/2 + 1/2 (b + w) Abs[(-(1/2) + Min[b, w])], + 1/2 (b + w) Abs[(-(1/2) + Min[b, w])] + Min[b, w]] +*) + HardAND[input_, weight_] := Or[input, Not[weight]] HardAND[input_/;VectorQ[input], weights_/;VectorQ[weights]] := Block[{}, diff --git a/tests/data/BinaryIrisData.txt b/tests/data/BinaryIrisData.txt new file mode 100644 index 0000000..430f463 --- /dev/null +++ b/tests/data/BinaryIrisData.txt @@ -0,0 +1,150 @@ +0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 +0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 +0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 +0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 +0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 +0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 +0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 +0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 +0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 +0 0 1 1 0 0 0 1 0 0 0 0 0 0 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b/tests/data/toy_data_2.txt @@ -0,0 +1,60 @@ +1 0 0 0 0 1 +0 1 0 0 0 1 +0 0 1 0 0 0 +0 0 0 1 0 0 +1 0 0 0 0 1 +0 1 0 0 0 1 +0 0 1 0 0 0 +0 0 0 1 0 0 +1 0 0 0 1 1 +0 1 0 0 1 1 +0 0 1 0 1 0 +0 0 0 1 1 1 +1 0 0 0 1 1 +0 1 0 0 1 1 +0 0 1 0 1 0 +0 0 0 1 1 1 +0 1 0 0 0 1 +0 0 0 1 1 1 +1 0 0 0 1 1 +0 0 1 0 1 0 +1 0 0 0 0 1 +0 1 0 0 0 1 +0 0 1 0 0 0 +0 0 0 1 0 0 +1 0 0 0 0 1 +0 1 0 0 0 1 +0 0 1 0 0 0 +0 0 0 1 0 0 +1 0 0 0 1 1 +0 1 0 0 1 1 +0 0 1 0 1 0 +0 0 0 1 1 1 +1 0 0 0 1 1 +0 1 0 0 1 1 +0 0 1 0 1 0 +0 0 0 1 1 1 +0 1 0 0 0 1 +0 0 0 1 1 1 +1 0 0 0 1 1 +0 0 1 0 1 0 +1 0 0 0 0 1 +0 1 0 0 0 1 +0 0 1 0 0 0 +0 0 0 1 0 0 +1 0 0 0 0 1 +0 1 0 0 0 1 +0 0 1 0 0 0 +0 0 0 1 0 0 +1 0 0 0 1 1 +0 1 0 0 1 1 +0 0 1 0 1 0 +0 0 0 1 1 1 +1 0 0 0 1 1 +0 1 0 0 1 1 +0 0 1 0 1 0 +0 0 0 1 1 1 +0 1 0 0 0 1 +0 0 0 1 1 1 +1 0 0 0 1 1 +0 0 1 0 1 0 \ No newline at end of file diff --git a/tests/test_hard_and.py b/tests/test_hard_and.py index e1854df..411bee1 100644 --- a/tests/test_hard_and.py +++ b/tests/test_hard_and.py @@ -9,64 +9,71 @@ from tests import utils -def test_include(): - test_data = [ - [[1.0, 1.0], 1.0], - [[1.0, 0.0], 0.0], - [[0.0, 0.0], 1.0], - [[0.0, 1.0], 1.0], - [[1.1, 1.0], 1.0], - [[1.1, 0.0], 0.0], - [[-0.1, 0.0], 1.0], - [[-0.1, 1.0], 1.0] - ] - for input, expected in test_data: - utils.check_consistency(hard_and.soft_and_include, hard_and.hard_and_include, - expected, input[0], input[1]) - - def test_neuron(): test_data = [ - [[1.0, 1.0], [1.0, 1.0], 1.0], - [[0.0, 0.0], [0.0, 0.0], 1.0], + [[1.0, 1.0], [1.0, 1.0], 0.75], + [[0.0, 0.0], [0.0, 0.0], 0.75], [[1.0, 0.0], [0.0, 1.0], 0.0], [[0.0, 1.0], [1.0, 0.0], 0.0], - [[0.0, 1.0], [0.0, 0.0], 1.0], - [[0.0, 1.0], [1.0, 1.0], 0.0] + [[0.0, 1.0], [0.0, 0.0], 0.75], + [[0.0, 1.0], [1.0, 1.0], 0.0], ] for input, weights, expected in test_data: + def soft(weights, input): return hard_and.soft_and_neuron(weights, input) def hard(weights, input): return hard_and.hard_and_neuron(weights, input) - utils.check_consistency(soft, hard, expected, - jax.numpy.array(weights), jax.numpy.array(input)) + utils.check_consistency( + soft, hard, expected, jax.numpy.array(weights), jax.numpy.array(input) + ) def test_layer(): test_data = [ - [[1.0, 0.0], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], - [0.0, 0.0]], [0.0, 0.0, 1.0, 1.0]], - [[1.0, 0.0], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], - [0.0, 0.2]], [0.0, 0.0, 1.0, 0.8]], - [[1.0, 0.4], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], - [0.0, 0.0]], [0.4, 0.4, 1.0, 1.0]], - [[0.0, 1.0], [[1.0, 1.0], [0.0, 0.8], [1.0, 0.0], - [0.0, 0.0]], [0.0, 1.0, 0.0, 1.0]], - [[0.0, 0.0], [[1.0, 0.01], [0.0, 1.0], [ - 1.0, 0.0], [0.0, 0.0]], [0.0, 0.0, 0.0, 1.0]] + [ + [1.0, 0.0], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [0.0, 0.0, 0.75, 0.75], + ], + [ + [1.0, 0.0], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.2]], + [0.0, 0.0, 0.75, 0.62], + ], + [ + [1.0, 0.4], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [0.42000002, 0.42000002, 0.75, 0.85] + ], + [ + [0.0, 1.0], + [[1.0, 1.0], [0.0, 0.8], [1.0, 0.0], [0.0, 0.0]], + [0.0, 0.75, 0.0, 0.75], + ], + [ + [0.0, 0.0], + [[1.0, 0.01], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [0.0, 0.0, 0.0, 0.75], + ], ] for input, weights, expected in test_data: + def soft(weights, input): return hard_and.soft_and_layer(weights, input) def hard(weights, input): return hard_and.hard_and_layer(weights, input) - utils.check_consistency(soft, hard, jax.numpy.array(expected), - jax.numpy.array(weights), jax.numpy.array(input)) + utils.check_consistency( + soft, + hard, + jax.numpy.array(expected), + jax.numpy.array(weights), + jax.numpy.array(input), + ) def test_and(): @@ -80,27 +87,17 @@ def test_net(type, x): hard_weights = harden.hard_weights(weights) test_data = [ - [ - [1.0, 1.0], - [1.0, 1.0, 1.0, 1.0] - ], - [ - [1.0, 0.0], - [0.53707814, 0.13892889, 0.7197356, 0.62835324] - ], - [ - [0.0, 1.0], - [0.35097015, 0.34810758, 0.04889798, 0.43687034] - ], - [ - [0.0, 0.0], - [0.35097015, 0.13892889, 0.04889798, 0.43687034] - ] + [[1.0, 1.0], [0.83774257, 0.7847322, 0.7622245, 0.8592176]], + [[1.0, 0.0], [0.50995696, 0.1640105, 0.57907575, 0.5403256]], + [[0.0, 1.0], [0.37712267, 0.37454504, 0.05992697, 0.45066008]], + [[0.0, 0.0], [0.37712267, 0.1640105, 0.05992697, 0.45066008]], ] for input, expected in test_data: # Check that the soft function performs as expected - assert jax.numpy.allclose(soft.apply( - weights, jax.numpy.array(input)), jax.numpy.array(expected)) + output = soft.apply(weights, jax.numpy.array(input)) + assert jax.numpy.allclose( + output, jax.numpy.array(expected) + ) # Check that the hard function performs as expected hard_input = harden.harden(jax.numpy.array(input)) @@ -130,17 +127,21 @@ def test_net(type, x): [1.0, 1.0, 1.0, 1.0], [0.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0], - [0.0, 1.0, 1.0, 1.0] + [0.0, 1.0, 1.0, 1.0], ] input = jax.numpy.array(x) output = jax.numpy.array(y) # Train the and layer tx = optax.sgd(0.1) - state = train_state.TrainState.create(apply_fn=jax.vmap( - soft.apply, in_axes=(None, 0)), params=weights, tx=tx) - grad_fn = jax.jit(jax.value_and_grad(lambda params, x, - y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2))) + state = train_state.TrainState.create( + apply_fn=jax.vmap(soft.apply, in_axes=(None, 0)), params=weights, tx=tx + ) + grad_fn = jax.jit( + jax.value_and_grad( + lambda params, x, y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2) + ) + ) for epoch in range(1, 100): loss, grads = grad_fn(state.params, input, output) state = state.apply_gradients(grads=grads) @@ -184,27 +185,36 @@ def test_net(type, x): assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and symbolic weights, but where the symbols can be evaluated - symbolic_input = ['True', 'False'] + symbolic_input = ["True", "False"] symbolic_weights = utils.make_symbolic(hard_weights) symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) - symbolic_output = symbolic_generation.eval_symbolic_expression( - symbolic_output) + symbolic_output = symbolic_generation.eval_symbolic_expression(symbolic_output) # Check that the symbolic result is the same as the hard result assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and non-symbolic weights - symbolic_input = ['x1', 'x2'] + symbolic_input = ["x1", "x2"] symbolic_output = symbolic.apply(hard_weights, symbolic_input) # Check the form of the symbolic expression - assert numpy.array_equal(symbolic_output, ['numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False))']) + assert numpy.array_equal( + symbolic_output, + [ + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), False)), numpy.logical_or(lax_reference.ne(x2, 0), True)), 0), False))", + ], + ) # Compute symbolic result with symbolic inputs and symbolic weights symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) # Check the form of the symbolic expression - assert numpy.array_equal(symbolic_output, ['numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0))))', - 'numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0))))', - 'numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0))))', - 'numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0))))']) + assert numpy.array_equal( + symbolic_output, + [ + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0))))", + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0))))", + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0))))", + "numpy.logical_and(numpy.logical_and(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(False, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(True, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(numpy.logical_and(numpy.logical_and(True, numpy.logical_or(lax_reference.ne(x1, 0), numpy.logical_not(lax_reference.ne(True, 0)))), numpy.logical_or(lax_reference.ne(x2, 0), numpy.logical_not(lax_reference.ne(False, 0)))), 0), numpy.logical_not(lax_reference.ne(True, 0))))", + ], + ) diff --git a/tests/test_hard_count.py b/tests/test_hard_count.py new file mode 100644 index 0000000..34ade8b --- /dev/null +++ b/tests/test_hard_count.py @@ -0,0 +1,53 @@ +import numpy +import jax + +from neurallogic import hard_count + +def test_soft_count(): + # 2 bits are high in a 7-bit input array, x + x = numpy.array([1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0]) + y = hard_count.soft_count(x) + # We expect a 8-bit output array, y, where y[5] is the only high soft-bit (indicating that 5 soft-bits are low in the input) + expected_output = numpy.array([0.25, 0.25, 0.25, 0.25, 0.25, 1., 0.25, 0.25]) + print("soft_count", y) + assert numpy.allclose(y, expected_output) + + # Same example as above, except instead of 0s and 1s, we have soft-bits + x = numpy.array([0.9, 0.1, 0.1, 0.1, 0.1, 0.9, 0.1]) + y = hard_count.soft_count(x) + # We expect an 8-bit output array, y, where y[5] is the only high soft-bit (indicating that 5 soft-bits are low in the input) + expected_output = numpy.array([0.32000002, 0.3, 0.3, 0.3, 0.3, 0.85999995, 0.3, 0.32000002]) + print("soft_count", y) + assert numpy.allclose(y, expected_output) + + x = numpy.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]) + y = hard_count.soft_count(x) + # We expect an 8-bit output array, y, where no y[0] is high (indicating that 0 soft-bits are low in the input) + expected_output = numpy.array([1., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25]) + print("soft_count", y) + assert numpy.allclose(y, expected_output) + + # Same example as above, except instead of 0s and 1s, we have soft-bits + x = numpy.array([0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9]) + y = hard_count.soft_count(x) + # We expect an 8-bit output array, y, where y[0] is high (indicating that 0 soft-bits are low in the input) + expected_output = numpy.array([0.88, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.32000002]) + print("soft_count", y) + assert numpy.allclose(y, expected_output) + + x = numpy.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]) + y = hard_count.soft_count(x) + # We expect an 8-bit output array, y, where y[7] is the only high soft-bit (indicating that 7 soft-bits are low in the input) + expected_output = numpy.array([0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 1.]) + print("soft_count", y) + assert numpy.allclose(y, expected_output) + + # Same example as above, except instead of 0s and 1s, we have soft-bits + x = numpy.array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) + y = hard_count.soft_count(x) + # We expect an 7-bit output array, y, where y[7] is the only high soft-bit (indicating that 7 soft-bits are low in the input) + expected_output = numpy.array([0.32000002, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.88]) + print("soft_count", y) + assert numpy.allclose(y, expected_output) + +# TODO: test soft_count == hard_count \ No newline at end of file diff --git a/tests/test_hard_majority.py b/tests/test_hard_majority.py index fc47b41..08330cb 100644 --- a/tests/test_hard_majority.py +++ b/tests/test_hard_majority.py @@ -2,6 +2,7 @@ import jax from neurallogic import hard_majority, harden, symbolic_generation +from tests import utils def test_majority_index(): @@ -19,50 +20,91 @@ def test_majority_index(): assert hard_majority.majority_index(12) == 5 -def test_soft_majority(): - assert hard_majority.soft_majority(numpy.array([1.0])) == 1.0 - assert hard_majority.soft_majority(numpy.array([2.0, 1.0])) == 1.0 - assert hard_majority.soft_majority(numpy.array([1.0, 3.0, 2.0])) == 2.0 - assert hard_majority.soft_majority( - numpy.array([2.0, 1.0, 4.0, 3.0])) == 2.0 - assert hard_majority.soft_majority( - numpy.array([1.0, 2.0, 3.0, 4.0, 5.0])) == 3.0 - assert hard_majority.soft_majority( - numpy.array([6.0, 3.0, 2.0, 4.0, 5.0, 1.0])) == 3.0 - assert hard_majority.soft_majority(numpy.array( - [7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0])) == 4.0 - assert hard_majority.soft_majority(numpy.array( - [2.0, 1.0, 4.0, 3.0, 6.0, 5.0, 8.0, 7.0])) == 4.0 - assert hard_majority.soft_majority(numpy.array( - [1.0, 2.0, 3.0, 5.0, 4.0, 6.0, 7.0, 9.0, 8.0])) == 5.0 - assert hard_majority.soft_majority(numpy.array( - [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0])) == 5.0 - assert hard_majority.soft_majority(numpy.array( - [11.0, 10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0])) == 6.0 - assert hard_majority.soft_majority(numpy.array( - [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0])) == 6.0 +def test_majority_bit(): + assert hard_majority.majority_bit(numpy.array([1.0])) == 1.0 + assert hard_majority.majority_bit(numpy.array([2.0, 1.0])) == 1.0 + assert hard_majority.majority_bit(numpy.array([1.0, 3.0, 2.0])) == 2.0 + assert hard_majority.majority_bit(numpy.array([2.0, 1.0, 4.0, 3.0])) == 2.0 + assert hard_majority.majority_bit(numpy.array([1.0, 2.0, 3.0, 4.0, 5.0])) == 3.0 + assert ( + hard_majority.majority_bit(numpy.array([6.0, 3.0, 2.0, 4.0, 5.0, 1.0])) == 3.0 + ) + assert ( + hard_majority.majority_bit(numpy.array([7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0])) + == 4.0 + ) + assert ( + hard_majority.majority_bit( + numpy.array([2.0, 1.0, 4.0, 3.0, 6.0, 5.0, 8.0, 7.0]) + ) + == 4.0 + ) + assert ( + hard_majority.majority_bit( + numpy.array([1.0, 2.0, 3.0, 5.0, 4.0, 6.0, 7.0, 9.0, 8.0]) + ) + == 5.0 + ) + assert ( + hard_majority.majority_bit( + numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]) + ) + == 5.0 + ) + assert ( + hard_majority.majority_bit( + numpy.array([11.0, 10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0]) + ) + == 6.0 + ) + assert ( + hard_majority.majority_bit( + numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0]) + ) + == 6.0 + ) def test_hard_majority(): assert hard_majority.hard_majority(numpy.array([True])) == True assert hard_majority.hard_majority(numpy.array([False])) == False assert hard_majority.hard_majority(numpy.array([True, False])) == False - assert hard_majority.hard_majority( - numpy.array([False, True, False])) == False - assert hard_majority.hard_majority( - numpy.array([True, False, True, False])) == False - assert hard_majority.hard_majority(numpy.array( - [False, True, False, True, False])) == False - assert hard_majority.hard_majority(numpy.array( - [True, True, True, False, True, False])) == True - assert hard_majority.hard_majority(numpy.array( - [True, False, False, True, True, True, False])) == True - assert hard_majority.hard_majority(numpy.array( - [False, True, False, True, False, True, False, True])) == False - assert hard_majority.hard_majority(numpy.array( - [True, True, True, True, True, False, True, True, True])) == True - assert hard_majority.hard_majority(numpy.array( - [True, False, False, False, False, False, True, True, True, True])) == False + assert hard_majority.hard_majority(numpy.array([False, True, False])) == False + assert hard_majority.hard_majority(numpy.array([True, False, True, False])) == False + assert ( + hard_majority.hard_majority(numpy.array([False, True, False, True, False])) + == False + ) + assert ( + hard_majority.hard_majority(numpy.array([True, True, True, False, True, False])) + == True + ) + assert ( + hard_majority.hard_majority( + numpy.array([True, False, False, True, True, True, False]) + ) + == True + ) + assert ( + hard_majority.hard_majority( + numpy.array([False, True, False, True, False, True, False, True]) + ) + == False + ) + assert ( + hard_majority.hard_majority( + numpy.array([True, True, True, True, True, False, True, True, True]) + ) + == True + ) + assert ( + hard_majority.hard_majority( + numpy.array( + [True, False, False, False, False, False, True, True, True, True] + ) + ) + == False + ) def test_soft_and_hard_majority_equivalence(): @@ -76,91 +118,191 @@ def test_soft_and_hard_majority_equivalence(): def test_soft_majority_layer(): - assert numpy.all(hard_majority.soft_majority_layer( - numpy.array([[2.0, 1.0], [1.0, 2.0]])) == numpy.array([1.0, 1.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0], [3.0, 2.0, 1.0]])) == numpy.array([2.0, 2.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0], [4.0, 3.0, 2.0, 1.0]])) == numpy.array([2.0, 2.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0], [5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([3.0, 3.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0, 6.0], [6.0, 5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([3.0, 3.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0], [7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([4.0, 4.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], [8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([4.0, 4.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], [9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([5.0, 5.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0], [10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([5.0, 5.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0], [11.0, 10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([6.0, 6.0])) - assert numpy.all(hard_majority.soft_majority_layer(numpy.array( - [[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0], [12.0, 11.0, 10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0]])) == numpy.array([6.0, 6.0])) + assert numpy.allclose( + hard_majority.soft_majority_layer(numpy.array([[0.0, 1.0], [1.0, 0.0]])), + numpy.array([0.25, 0.25]), + ) + assert numpy.allclose( + hard_majority.soft_majority_layer( + numpy.array([[0.0, 1.0, 1.0], [1.0, 0.0, 0.0]]) + ), + numpy.array([0.8333334, 0.16666667]), + ) + assert numpy.allclose( + hard_majority.soft_majority_layer( + numpy.array([[1.0, 0.0, 1.0, 0.0], [1.0, 0.0, 1.0, 1.0]]) + ), + numpy.array([0.25, 0.875]), + ) + assert numpy.allclose( + hard_majority.soft_majority_layer( + numpy.array([[0.0, 1.0, 1.0, 0.0, 0.0], [1.0, 1.0, 0.0, 1.0, 1.0]]) + ), + numpy.array([0.2, 0.9]), + ) + assert numpy.allclose( + hard_majority.soft_majority_layer( + numpy.array( + [[0.0, 1.0, 0.0, 1.0, 0.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, 0.0]] + ) + ), + numpy.array([0.25, 0.9166667]), + ) + assert numpy.allclose( + hard_majority.soft_majority_layer( + numpy.array( + [ + [1.0, 0.0, 0.0, 0.0, 0.0, 0.8, 0.4], + [1.0, 0.9, 0.8, 0.45, 0.48, 0.51, 0.52], + ] + ) + ), + numpy.array([0.15714286, 0.51331425]), + ) def test_hard_majority_layer(): - assert numpy.all(hard_majority.hard_majority_layer(numpy.array( - [[True, False], [False, True]])) == numpy.array([False, False])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array( - [[True, False, True], [True, False, False]])) == numpy.array([True, False])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array( - [[True, False, True, False], [False, True, False, True]])) == numpy.array([False, False])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array( - [[True, False, True, False, True], [True, False, True, False, True]])) == numpy.array([True, True])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array([[True, False, True, False, True, False], [ - False, True, False, True, False, True]])) == numpy.array([False, False])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array([[True, False, True, False, True, False, True], [ - True, False, True, False, True, False, False]])) == numpy.array([True, False])) - - assert numpy.all(hard_majority.hard_majority_layer(numpy.array([[True, False], [ - False, True], [False, True]])) == numpy.array([False, False, False])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array([[True, False, True], [ - True, False, True], [True, False, True]])) == numpy.array([True, True, True])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array([[True, False, True, False], [ - False, True, False, True], [False, True, False, True]])) == numpy.array([False, False, False])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array([[True, False, True, False, True], [ - True, False, True, False, True], [True, False, True, False, True]])) == numpy.array([True, True, True])) - assert numpy.all(hard_majority.hard_majority_layer(numpy.array([[True, False, True, False, True, False], [ - False, True, False, True, False, True], [False, True, False, True, False, True]])) == numpy.array([False, False, False])) - - -def test_majority_layer(): - soft, hard, symbolic = hard_majority.soft_majority_layer, hard_majority.hard_majority_layer, hard_majority.symbolic_majority_layer + assert numpy.all( + hard_majority.hard_majority_layer(numpy.array([[True, False], [False, True]])) + == numpy.array([False, False]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array([[True, False, True], [True, False, False]]) + ) + == numpy.array([True, False]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array([[True, False, True, False], [False, True, False, True]]) + ) + == numpy.array([False, False]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array( + [[True, False, True, False, True], [True, False, True, False, True]] + ) + ) + == numpy.array([True, True]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array( + [ + [True, False, True, False, True, False], + [False, True, False, True, False, True], + ] + ) + ) + == numpy.array([False, False]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array( + [ + [True, False, True, False, True, False, True], + [True, False, True, False, True, False, False], + ] + ) + ) + == numpy.array([True, False]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array([[True, False], [False, True], [False, True]]) + ) + == numpy.array([False, False, False]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array([[True, False, True], [True, False, True], [True, False, True]]) + ) + == numpy.array([True, True, True]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array( + [ + [True, False, True, False], + [False, True, False, True], + [False, True, False, True], + ] + ) + ) + == numpy.array([False, False, False]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array( + [ + [True, False, True, False, True], + [True, False, True, False, True], + [True, False, True, False, True], + ] + ) + ) + == numpy.array([True, True, True]) + ) + assert numpy.all( + hard_majority.hard_majority_layer( + numpy.array( + [ + [True, False, True, False, True, False], + [False, True, False, True, False, True], + [False, True, False, True, False, True], + ] + ) + ) + == numpy.array([False, False, False]) + ) + + +def test_layer(): test_data = [ - [ - [[0.8, 0.1, 0.4], [1.0, 0.0, 0.3]], - [0.4, 0.3] - ], + [[[0.8, 0.1, 0.4], [1.0, 0.0, 0.3]], [0.44333333, 0.3866667]], [ [[0.8, 0.1, 0.4], [1.0, 0.0, 0.3], [0.0, 0.0, 0.0]], - [0.4, 0.3, 0.0] + [0.44333333, 0.3866667, 0.0], ], [ [[0.8, 0.1, 0.4], [1.0, 0.0, 0.3], [0.8, 0.9, 0.1], [0.2, 0.01, 0.45]], - [0.4, 0.3, 0.8, 0.2] + [0.44333333, 0.3866667, 0.68, 0.266], ], [ - [[0.8, 0.1, 0.4], [1.0, 0.0, 0.3], [0.8, 0.9, 0.1], [0.2, 0.01, 0.45], [0.0, 0.0, 0.0]], - [0.4, 0.3, 0.8, 0.2, 0.0] + [ + [0.8, 0.1, 0.4], + [1.0, 0.0, 0.3], + [0.8, 0.9, 0.1], + [0.2, 0.01, 0.45], + [0.0, 0.0, 0.0], + ], + [0.44333333, 0.3866667, 0.68, 0.266, 0.0], ], [ - [[0.3, 0.93, 0.01, 0.5], [0.2, 0.01, 0.45, 0.1], [0.8, 0.9, 0.1, 0.2], [0.8, 0.1, 0.4, 0.3], [0.0, 0.0, 0.0, 0.0]], - [0.3, 0.1, 0.2, 0.3, 0.0] - ] + [ + [0.3, 0.93, 0.01, 0.5], + [0.2, 0.01, 0.45, 0.1], + [0.8, 0.9, 0.1, 0.2], + [0.8, 0.1, 0.4, 0.3], + [0.0, 0.0, 0.0, 0.0], + ], + [0.38700002, 0.176, 0.35000002, 0.38, 0.0], + ], ] - + for input, expected in test_data: - input = jax.numpy.array(input) - expected = jax.numpy.array(expected) - soft_output = soft(input) - assert jax.numpy.array_equal(soft_output, expected) - hard_output = hard(harden.harden(input)) - assert jax.numpy.array_equal(hard_output, harden.harden(expected)) - jaxpr = symbolic_generation.make_symbolic_jaxpr(symbolic, harden.harden(input)) - symbolic_output = symbolic_generation.symbolic_expression(jaxpr, harden.harden(input)) - assert jax.numpy.array_equal(symbolic_output, harden.harden(expected)) - -# TODO: test training the hard majority layer \ No newline at end of file + + def soft(input): + return hard_majority.soft_majority_layer(input) + + def hard(input): + return hard_majority.hard_majority_layer(input) + + utils.check_consistency( + soft, hard, jax.numpy.array(expected), jax.numpy.array(input) + ) + + +# TODO: test training the hard majority layer diff --git a/tests/test_hard_masks.py b/tests/test_hard_masks.py new file mode 100644 index 0000000..dcf8a6a --- /dev/null +++ b/tests/test_hard_masks.py @@ -0,0 +1,280 @@ +import jax +import numpy +from jax import random + +from neurallogic import hard_masks, harden, neural_logic_net +from tests import utils + + +def test_mask_to_true(): + test_data = [ + [[1.0, 1.0], 1.0], + [[1.0, 0.0], 0.0], + [[0.0, 0.0], 1.0], + [[0.0, 1.0], 1.0], + [[1.1, 1.0], 1.0], + [[1.1, 0.0], 0.0], + [[-0.1, 0.0], 1.0], + [[-0.1, 1.0], 1.0], + ] + for input, expected in test_data: + utils.check_consistency( + hard_masks.soft_mask_to_true, + hard_masks.hard_mask_to_true, + expected, + input[0], + input[1], + ) + + +def test_mask_to_true_neuron(): + test_data = [ + [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]], + [[0.0, 0.0], [0.0, 0.0], [1.0, 1.0]], + [[1.0, 0.0], [0.0, 1.0], [1.0, 0.0]], + [[0.0, 1.0], [1.0, 0.0], [0.0, 1.0]], + [[0.0, 1.0], [0.0, 0.0], [1.0, 1.0]], + [[0.0, 1.0], [1.0, 1.0], [0.0, 1.0]], + ] + for input, weights, expected in test_data: + + def soft(weights, input): + return hard_masks.soft_mask_to_true_neuron(weights, input) + + def hard(weights, input): + return hard_masks.hard_mask_to_true_neuron(weights, input) + + utils.check_consistency( + soft, hard, expected, jax.numpy.array(weights), jax.numpy.array(input) + ) + + +def test_mask_to_true_layer(): + test_data = [ + [ + [1.0, 0.0], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.2]], + [[1.0, 0.0], [1.0, 0.0], [1.0, 1.0], [1.0, 0.8]], + ], + [ + [1.0, 0.4], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [[1.0, 0.4], [1.0, 0.4], [1.0, 1.0], [1.0, 1.0]], + ], + [ + [0.0, 1.0], + [[1.0, 1.0], [0.0, 0.8], [1.0, 0.0], [0.0, 0.0]], + [[0.0, 1.0], [1.0, 1.0], [0.0, 1.0], [1.0, 1.0]], + ], + [ + [0.0, 0.0], + [[1.0, 0.01], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [[0.0, 0.99], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]], + ], + ] + for input, weights, expected in test_data: + + def soft(weights, input): + return hard_masks.soft_mask_to_true_layer(weights, input) + + def hard(weights, input): + return hard_masks.hard_mask_to_true_layer(weights, input) + + utils.check_consistency( + soft, + hard, + jax.numpy.array(expected), + jax.numpy.array(weights), + jax.numpy.array(input), + ) + + +def test_mask_to_true_net(): + def test_net(type, x): + x = hard_masks.mask_to_true_layer(type)(4)(x) + x = x.ravel() + return x + + soft, hard, symbolic = neural_logic_net.net(test_net) + weights = soft.init(random.PRNGKey(0), [0.0, 0.0]) + hard_weights = harden.hard_weights(weights) + + test_data = [ + [ + [1.0, 1.0], + [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], + ], + [ + [1.0, 0.0], + [1.0, 0.17739451, 1.0, 0.77752244, 1.0, 0.11280203, 1.0, 0.43465567], + ], + [ + [0.0, 1.0], + [0.6201445, 1.0, 0.7178699, 1.0, 0.29197645, 1.0, 0.41213453, 1.0], + ], + [ + [0.0, 0.0], + [ + 0.6201445, + 0.17739451, + 0.7178699, + 0.77752244, + 0.29197645, + 0.11280203, + 0.41213453, + 0.43465567, + ], + ], + ] + for input, expected in test_data: + # Check that the soft function performs as expected + soft_output = soft.apply(weights, jax.numpy.array(input)) + expected_output = jax.numpy.array(expected) + assert jax.numpy.allclose(soft_output, expected_output) + + # Check that the hard function performs as expected + hard_input = harden.harden(jax.numpy.array(input)) + hard_expected = harden.harden(jax.numpy.array(expected)) + hard_output = hard.apply(hard_weights, hard_input) + assert jax.numpy.allclose(hard_output, hard_expected) + + # Check that the symbolic function performs as expected + symbolic_output = symbolic.apply(hard_weights, hard_input) + assert numpy.allclose(symbolic_output, hard_expected) + + +def test_mask_to_false(): + test_data = [ + [[1.0, 1.0], 1.0], + [[1.0, 0.0], 0.0], + [[0.0, 0.0], 0.0], + [[0.0, 1.0], 0.0], + [[1.1, 1.0], 1.0], + [[1.1, 0.0], 0.0], + [[-0.1, 0.0], 0.0], + [[-0.1, 1.0], 0.0], + ] + for input, expected in test_data: + utils.check_consistency( + hard_masks.soft_mask_to_false, + hard_masks.hard_mask_to_false, + expected, + input[0], + input[1], + ) + + +def test_mask_to_false_neuron(): + test_data = [ + [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]], + [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]], + [[1.0, 0.0], [0.0, 1.0], [0.0, 0.0]], + [[0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [[0.0, 1.0], [0.0, 0.0], [0.0, 0.0]], + [[0.0, 1.0], [1.0, 1.0], [0.0, 1.0]], + ] + for input, weights, expected in test_data: + + def soft(weights, input): + return hard_masks.soft_mask_to_false_neuron(weights, input) + + def hard(weights, input): + return hard_masks.hard_mask_to_false_neuron(weights, input) + + utils.check_consistency( + soft, hard, expected, jax.numpy.array(weights), jax.numpy.array(input) + ) + + +def test_mask_to_false_layer(): + test_data = [ + [ + [1.0, 0.0], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.2]], + [[1.0, 0.0], [0.0, 0.0], [1.0, 0.0], [0.0, 0.0]], + ], + [ + [1.0, 0.4], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [[1.0, 0.39999998], [0.0, 0.39999998], [1.0, 0.0], [0.0, 0.0]], + ], + [ + [0.0, 1.0], + [[1.0, 1.0], [0.0, 0.8], [1.0, 0.0], [0.0, 0.0]], + [[0.0, 1.0], [0.0, 0.8], [0.0, 0.0], [0.0, 0.0]], + ], + [ + [0.0, 0.0], + [[1.0, 0.01], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]], + ], + ] + for input, weights, expected in test_data: + + def soft(weights, input): + return hard_masks.soft_mask_to_false_layer(weights, input) + + def hard(weights, input): + return hard_masks.hard_mask_to_false_layer(weights, input) + + utils.check_consistency( + soft, + hard, + jax.numpy.array(expected), + jax.numpy.array(weights), + jax.numpy.array(input), + ) + + +def test_mask_to_false_net(): + def test_net(type, x): + x = hard_masks.mask_to_false_layer(type)(4)(x) + x = x.ravel() + return x + + soft, hard, symbolic = neural_logic_net.net(test_net) + weights = soft.init(random.PRNGKey(0), [0.0, 0.0]) + hard_weights = harden.hard_weights(weights) + + test_data = [ + [ + [1.0, 1.0], + [ + 0.3798555, + 0.8226055, + 0.28213012, + 0.22247756, + 0.70802355, + 0.887198, + 0.5878655, + 0.56534433, + ], + ], + [ + [1.0, 0.0], + [0.3798555, 0.0, 0.28213012, 0.0, 0.70802355, 0.0, 0.5878655, 0.0], + ], + [ + [0.0, 1.0], + [0.0, 0.8226055, 0.0, 0.22247756, 0.0, 0.887198, 0.0, 0.56534433] + ], + [ + [0.0, 0.0], + [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], + ], + ] + for input, expected in test_data: + # Check that the soft function performs as expected + soft_output = soft.apply(weights, jax.numpy.array(input)) + expected_output = jax.numpy.array(expected) + assert jax.numpy.allclose(soft_output, expected_output) + + # Check that the hard function performs as expected + hard_input = harden.harden(jax.numpy.array(input)) + hard_expected = harden.harden(jax.numpy.array(expected)) + hard_output = hard.apply(hard_weights, hard_input) + assert jax.numpy.allclose(hard_output, hard_expected) + + # Check that the symbolic function performs as expected + symbolic_output = symbolic.apply(hard_weights, hard_input) + assert numpy.allclose(symbolic_output, hard_expected) diff --git a/tests/test_hard_not.py b/tests/test_hard_not.py index 37ddaa9..bdd10a1 100644 --- a/tests/test_hard_not.py +++ b/tests/test_hard_not.py @@ -1,7 +1,7 @@ import jax -import jax.numpy as jnp import numpy import optax +from flax import linen as nn from flax.training import train_state from jax import random @@ -38,14 +38,13 @@ def test_neuron(): for input, weights, expected in test_data: def soft(weights, input): - return hard_not.hard_not_neuron(weights, input) + return hard_not.soft_not_neuron(weights, input) def hard(weights, input): return hard_not.hard_not_neuron(weights, input) utils.check_consistency( - soft, hard, expected, jax.numpy.array( - weights), jax.numpy.array(input) + soft, hard, expected, jax.numpy.array(weights), jax.numpy.array(input) ) @@ -91,7 +90,7 @@ def hard(weights, input): def test_not(): def test_net(type, x): - x = hard_not.not_layer(type)(4)(x) + x = hard_not.not_layer(type)(4, weights_init=nn.initializers.uniform(1.0))(x) x = x.ravel() return x @@ -156,8 +155,7 @@ def test_net(type, x): for input, expected in test_data: # Check that the soft function performs as expected assert jax.numpy.allclose( - soft.apply(weights, jax.numpy.array( - input)), jax.numpy.array(expected) + soft.apply(weights, jax.numpy.array(input)), jax.numpy.array(expected) ) # Check that the hard function performs as expected @@ -200,8 +198,7 @@ def test_net(type, x): ) grad_fn = jax.jit( jax.value_and_grad( - lambda params, x, y: jax.numpy.mean( - (state.apply_fn(params, x) - y) ** 2) + lambda params, x, y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2) ) ) for epoch in range(1, 100): @@ -252,8 +249,7 @@ def test_net(type, x): symbolic_input = ["True", "False"] symbolic_weights = utils.make_symbolic(hard_weights) symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) - symbolic_output = symbolic_generation.eval_symbolic_expression( - symbolic_output) + symbolic_output = symbolic_generation.eval_symbolic_expression(symbolic_output) # Check that the symbolic result is the same as the hard result assert numpy.array_equal(symbolic_output, hard_result) @@ -262,38 +258,41 @@ def test_net(type, x): symbolic_output = symbolic.apply(hard_weights, symbolic_input) # Check the form of the symbolic expression assert numpy.array_equal( - symbolic_output, ['numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))'] + symbolic_output, + [ + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), True)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), False)), 0), False))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), False)), 0), False))", + ], ) # Compute symbolic result with symbolic inputs and symbolic weights @@ -301,36 +300,38 @@ def test_net(type, x): # Check the form of the symbolic expression assert numpy.array_equal( symbolic_output, - ['numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))'] + [ + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_not(numpy.logical_xor(lax_reference.ne(numpy.logical_not(numpy.logical_xor(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0)))", + ], ) diff --git a/tests/test_hard_or.py b/tests/test_hard_or.py index 6f550fe..9badb01 100644 --- a/tests/test_hard_or.py +++ b/tests/test_hard_or.py @@ -9,62 +9,66 @@ from tests import utils -def test_include(): - test_data = [ - [[1.0, 1.0], 1.0], - [[1.0, 0.0], 0.0], - [[0.0, 0.0], 0.0], - [[0.0, 1.0], 0.0], - [[1.1, 1.0], 1.0], - [[1.1, 0.0], 0.0], - [[-0.1, 0.0], 0.0], - [[-0.1, 1.0], 0.0] - ] - for input, expected in test_data: - utils.check_consistency(hard_or.soft_or_include, hard_or.hard_or_include, - expected, input[0], input[1]) - - def test_neuron(): test_data = [ [[1.0, 1.0], [1.0, 1.0], 1.0], [[0.0, 0.0], [0.0, 0.0], 0.0], - [[1.0, 0.0], [0.0, 1.0], 0.0], - [[0.0, 1.0], [1.0, 0.0], 0.0], - [[0.0, 1.0], [0.0, 0.0], 0.0], - [[0.0, 1.0], [1.0, 1.0], 1.0] + [[1.0, 0.0], [0.0, 1.0], 0.25], + [[0.0, 1.0], [1.0, 0.0], 0.25], + [[0.0, 1.0], [0.0, 0.0], 0.25], + [[0.0, 1.0], [1.0, 1.0], 1.0], ] for input, weights, expected in test_data: + def soft(weights, input): return hard_or.soft_or_neuron(weights, input) def hard(weights, input): return hard_or.hard_or_neuron(weights, input) - utils.check_consistency(soft, hard, expected, - jax.numpy.array(weights), jax.numpy.array(input)) + utils.check_consistency( + soft, hard, expected, jax.numpy.array(weights), jax.numpy.array(input) + ) def test_layer(): test_data = [ - [[1.0, 0.0], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], - [0.0, 0.2]], [1.0, 0.0, 1.0, 0.0]], - [[1.0, 0.4], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], - [0.0, 0.0]], [1.0, 0.39999998, 1.0, 0.0]], - [[0.0, 1.0], [[1.0, 1.0], [0.0, 0.8], [1.0, 0.0], - [0.0, 0.0]], [1.0, 0.8, 0.0, 0.0]], - [[0.0, 0.0], [[1.0, 0.01], [0.0, 1.0], [ - 1.0, 0.0], [0.0, 0.0]], [0.0, 0.0, 0.0, 0.0]] + [ + [1.0, 0.0], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.2]], + [1., 0.25, 1., 0.25], + ], + [ + [1.0, 0.4], + [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [1., 0.47, 1., 0.25], + ], + [ + [0.0, 1.0], + [[1.0, 1.0], [0.0, 0.8], [1.0, 0.0], [0.0, 0.0]], + [1., 0.77, 0.25, 0.25], + ], + [ + [0.0, 0.0], + [[1.0, 0.01], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], + [0.25, 0.25, 0.25, 0.], + ], ] for input, weights, expected in test_data: + def soft(weights, input): return hard_or.soft_or_layer(weights, input) def hard(weights, input): return hard_or.hard_or_layer(weights, input) - utils.check_consistency(soft, hard, jax.numpy.array(expected), - jax.numpy.array(weights), jax.numpy.array(input)) + utils.check_consistency( + soft, + hard, + jax.numpy.array(expected), + jax.numpy.array(weights), + jax.numpy.array(input), + ) def test_or(): @@ -78,27 +82,19 @@ def test_net(type, x): hard_weights = harden.hard_weights(weights) test_data = [ - [ - [1.0, 1.0], - [0.45491087, 0.36511207, 0.62628365, 0.95989954] - ], - [ - [1.0, 0.0], - [0.2715416, 0.03128195, 0.01773429, 0.5896025] - ], - [ - [0.0, 1.0], - [0.45491087, 0.36511207, 0.62628365, 0.95989954] - ], - [ - [0.0, 0.0], - [0.0, 0.0, 0.0, 0.0] - ] + [[1.0, 1.0], [0.4877112, 0.45718065, 0.6026865, 0.95067847]], + [[1.0, 0.0], [0.41678876, 0.27297217, 0.26314348, 0.57121617]], + [[0.0, 1.0], [0.4877112, 0.45718065, 0.6026865, 0.95067847]], + [[0.0, 0.0], [0.11372772, 0.09127802, 0.15657091, 0.23997489]], ] for input, expected in test_data: # Check that the soft function performs as expected - assert jax.numpy.allclose(soft.apply( - weights, jax.numpy.array(input)), jax.numpy.array(expected)) + output = soft.apply(weights, jax.numpy.array(input)) + print("output", output) + print("expected", expected) + assert jax.numpy.allclose( + output, jax.numpy.array(expected) + ) # Check that the hard function performs as expected hard_input = harden.harden(jax.numpy.array(input)) @@ -128,18 +124,22 @@ def test_net(type, x): [1.0, 0.0, 1.0, 1.0], [1.0, 0.0, 1.0, 0.0], [1.0, 0.0, 0.0, 1.0], - [0.0, 0.0, 0.0, 0.0] + [0.0, 0.0, 0.0, 0.0], ] input = jax.numpy.array(x) output = jax.numpy.array(y) # Train the or layer tx = optax.sgd(0.1) - state = train_state.TrainState.create(apply_fn=jax.vmap( - soft.apply, in_axes=(None, 0)), params=weights, tx=tx) - grad_fn = jax.jit(jax.value_and_grad(lambda params, x, - y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2))) - for epoch in range(1, 100): + state = train_state.TrainState.create( + apply_fn=jax.vmap(soft.apply, in_axes=(None, 0)), params=weights, tx=tx + ) + grad_fn = jax.jit( + jax.value_and_grad( + lambda params, x, y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2) + ) + ) + for epoch in range(1, 500): loss, grads = grad_fn(state.params, input, output) state = state.apply_gradients(grads=grads) @@ -151,6 +151,8 @@ def test_net(type, x): hard_input = harden.harden(jax.numpy.array(input)) hard_expected = harden.harden(jax.numpy.array(expected)) hard_result = hard.apply(hard_weights, hard_input) + print("hard expected", hard_expected) + print("hard result", hard_result) assert jax.numpy.allclose(hard_result, hard_expected) symbolic_output = symbolic.apply(hard_weights, hard_input) assert jax.numpy.array_equal(symbolic_output, hard_expected) @@ -182,27 +184,36 @@ def test_net(type, x): assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and symbolic weights, but where the symbols can be evaluated - symbolic_input = ['True', 'False'] + symbolic_input = ["True", "False"] symbolic_weights = utils.make_symbolic(hard_weights) symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) - symbolic_output = symbolic_generation.eval_symbolic_expression( - symbolic_output) + symbolic_output = symbolic_generation.eval_symbolic_expression(symbolic_output) # Check that the symbolic result is the same as the hard result assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and non-symbolic weights - symbolic_input = ['x1', 'x2'] + symbolic_input = ["x1", "x2"] symbolic_output = symbolic.apply(hard_weights, symbolic_input) # Check the form of the symbolic expression - assert numpy.array_equal(symbolic_output, ['numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False))', - 'numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))']) + assert numpy.array_equal( + symbolic_output, + [ + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False))", + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))", + ], + ) # Compute symbolic result with symbolic inputs and symbolic weights symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) # Check the form of the symbolic expression - assert numpy.array_equal(symbolic_output, ['numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))']) + assert numpy.array_equal( + symbolic_output, + [ + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_or(numpy.logical_or(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_or(numpy.logical_or(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + ], + ) diff --git a/tests/test_hard_xor.py b/tests/test_hard_xor.py index 8bf0b8f..01dae84 100644 --- a/tests/test_hard_xor.py +++ b/tests/test_hard_xor.py @@ -1,7 +1,6 @@ import jax import numpy import optax -from flax import linen as nn from flax.training import train_state from jax import random @@ -9,53 +8,36 @@ from tests import utils -def test_include(): - test_data = [ - [[1.0, 1.0], 1.0], - [[1.0, 0.0], 0.0], - [[0.0, 0.0], 0.0], - [[0.0, 1.0], 0.0], - [[1.1, 1.0], 1.0], - [[1.1, 0.0], 0.0], - [[-0.1, 0.0], 0.0], - [[-0.1, 1.0], 0.0] - ] - for input, expected in test_data: - utils.check_consistency(hard_xor.soft_xor_include, hard_xor.hard_xor_include, - expected, input[0], input[1]) - - def test_neuron(): test_data = [ [[1.0, 1.0], [1.0, 1.0], 0.0], [[0.0, 0.0], [1.0, 1.0], 0.0], [[1.0, 0.0], [1.0, 1.0], 1.0], [[0.0, 1.0], [1.0, 1.0], 1.0], - [[1.0, 1.0], [0.0, 1.0], 1.0], [[0.0, 0.0], [0.0, 1.0], 0.0], [[1.0, 0.0], [0.0, 1.0], 0.0], [[0.0, 1.0], [0.0, 1.0], 1.0], - [[1.0, 1.0], [1.0, 0.0], 1.0], [[0.0, 0.0], [1.0, 0.0], 0.0], [[1.0, 0.0], [1.0, 0.0], 1.0], [[0.0, 1.0], [1.0, 0.0], 0.0], - [[1.0, 1.0], [0.0, 0.0], 0.0], [[0.0, 0.0], [0.0, 0.0], 0.0], [[1.0, 0.0], [0.0, 0.0], 0.0], - [[0.0, 1.0], [0.0, 0.0], 0.0] + [[0.0, 1.0], [0.0, 0.0], 0.0], ] for input, weights, expected in test_data: + def soft(weights, input): return hard_xor.soft_xor_neuron(weights, input) def hard(weights, input): return hard_xor.hard_xor_neuron(weights, input) - utils.check_consistency(soft, hard, expected, - jax.numpy.array(weights), jax.numpy.array(input)) + utils.check_consistency( + soft, hard, expected, jax.numpy.array(weights), jax.numpy.array(input) + ) def test_layer(): @@ -63,38 +45,44 @@ def test_layer(): [ [1.0, 0.0], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.2]], - [1.0, 0.0, 1.0, 0.0] + [1.0, 0.0, 1.0, 0.0], ], [ [1.0, 0.4], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], - [0.6, 0.39999998, 1.0, 0.0] + [0.6, 0.39999998, 1.0, 0.0], ], [ [0.0, 1.0], [[1.0, 1.0], [0.0, 0.8], [1.0, 0.0], [0.0, 0.0]], - [1.0, 0.8, 0.0, 0.0] + [1.0, 0.8, 0.0, 0.0], ], [ [0.0, 0.0], [[1.0, 0.01], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], - [0.0, 0.0, 0.0, 0.0] + [0.0, 0.0, 0.0, 0.0], ], [ [0.8, 0.6], [[1.0, 1.0], [0.0, 1.0], [1.0, 0.0], [0.0, 0.0]], - [0.39999998, 0.6, 0.8, 0.0] - ] + [0.39999998, 0.6, 0.8, 0.0], + ], ] for input, weights, expected in test_data: + def soft(weights, input): return hard_xor.soft_xor_layer(weights, input) def hard(weights, input): return hard_xor.hard_xor_layer(weights, input) - utils.check_consistency(soft, hard, jax.numpy.array(expected), - jax.numpy.array(weights), jax.numpy.array(input)) + utils.check_consistency( + soft, + hard, + jax.numpy.array(expected), + jax.numpy.array(weights), + jax.numpy.array(input), + ) def test_xor(): @@ -108,22 +96,10 @@ def test_net(type, x): hard_weights = harden.hard_weights(weights) test_data = [ - [ - [1.0, 1.0], - [0.56627953, 0.5280515, 0.18560958, 0.7154212] - ], - [ - [1.0, 0.0], - [0.38767397, 0.99864066, 0.8143904, 0.17714691] - ], - [ - [0.0, 1.0], - [0.56627953, 0.4719485, 0.8841522, 0.7154212] - ], - [ - [0.0, 0.0], - [0.0, 0.0, 0.0, 0.0] - ] + [[1.0, 1.0], [0.56627953, 0.5280515, 0.18560958, 0.7154212]], + [[1.0, 0.0], [0.38767397, 0.99864066, 0.8143904, 0.17714691]], + [[0.0, 1.0], [0.56627953, 0.4719485, 0.8841522, 0.7154212]], + [[0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], ] for input, expected in test_data: # Check that the soft function performs as expected @@ -159,17 +135,21 @@ def test_net(type, x): [0.0, 1.0, 1.0, 0.0], [1.0, 0.0, 1.0, 0.0], [1.0, 1.0, 0.0, 0.0], - [0.0, 0.0, 0.0, 0.0] + [0.0, 0.0, 0.0, 0.0], ] input = jax.numpy.array(x) output = jax.numpy.array(y) # Train the xor layer tx = optax.sgd(0.1) - state = train_state.TrainState.create(apply_fn=jax.vmap( - soft.apply, in_axes=(None, 0)), params=weights, tx=tx) - grad_fn = jax.jit(jax.value_and_grad(lambda params, x, - y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2))) + state = train_state.TrainState.create( + apply_fn=jax.vmap(soft.apply, in_axes=(None, 0)), params=weights, tx=tx + ) + grad_fn = jax.jit( + jax.value_and_grad( + lambda params, x, y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2) + ) + ) for epoch in range(1, 100): loss, grads = grad_fn(state.params, input, output) state = state.apply_gradients(grads=grads) @@ -213,27 +193,36 @@ def test_net(type, x): assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and symbolic weights, but where the symbols can be evaluated - symbolic_input = ['True', 'True'] + symbolic_input = ["True", "True"] symbolic_weights = utils.make_symbolic(hard_weights) symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) - symbolic_output = symbolic_generation.eval_symbolic_expression( - symbolic_output) + symbolic_output = symbolic_generation.eval_symbolic_expression(symbolic_output) # Check that the symbolic result is the same as the hard result assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and non-symbolic weights - symbolic_input = ['x1', 'x2'] + symbolic_input = ["x1", "x2"] symbolic_output = symbolic.apply(hard_weights, symbolic_input) # Check the form of the symbolic expression - assert numpy.array_equal(symbolic_output, ['numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False))', - 'numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))', - 'numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))']) + assert numpy.array_equal( + symbolic_output, + [ + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False))", + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))", + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), False)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), True)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), False)), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), False)), numpy.logical_and(lax_reference.ne(x2, 0), True)), 0), True))", + ], + ) # Compute symbolic result with symbolic inputs and symbolic weights symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) # Check the form of the symbolic expression - assert numpy.array_equal(symbolic_output, ['numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))', - 'numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))', - 'numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))']) + assert numpy.array_equal( + symbolic_output, + [ + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0)))", + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + "numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(False, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(True, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(numpy.logical_xor(numpy.logical_xor(False, numpy.logical_and(lax_reference.ne(x1, 0), lax_reference.ne(False, 0))), numpy.logical_and(lax_reference.ne(x2, 0), lax_reference.ne(True, 0))), 0), lax_reference.ne(True, 0)))", + ], + ) diff --git a/tests/test_iris.py b/tests/test_iris.py new file mode 100644 index 0000000..10bda81 --- /dev/null +++ b/tests/test_iris.py @@ -0,0 +1,431 @@ +from pathlib import Path + +import jax +import ml_collections +import numpy +import optax +import scipy +import pytest +from flax.training import train_state +from jax.config import config +from tqdm import tqdm + +from neurallogic import ( + hard_and, + hard_dropout, + hard_majority, + hard_masks, + hard_not, + hard_or, + hard_xor, + hard_count, + harden, + harden_layer, + neural_logic_net, + real_encoder, + initialization, + hard_vmap, + hard_concatenate, + symbolic_primitives +) +from tests import utils + +config.update("jax_enable_x64", True) + +def check_symbolic(nets, data, trained_state): + x_training, y_training, x_test, y_test = data + _, hard, symbolic = nets + _, test_loss, test_accuracy = apply_model_with_grad(trained_state, x_test, y_test) + print( + "soft_net: final test_loss: %.4f, final test_accuracy: %.2f" + % (test_loss, test_accuracy * 100) + ) + hard_weights = harden.hard_weights(trained_state.params) + hard_trained_state = train_state.TrainState.create( + apply_fn=hard.apply, params=hard_weights, tx=optax.sgd(1.0, 1.0) + ) + hard_input = harden.harden(x_test) + hard_test_accuracy = apply_hard_model(hard_trained_state, hard_input, y_test) + print("hard_net: final test_accuracy: %.2f" % (hard_test_accuracy * 100)) + assert numpy.isclose(test_accuracy, hard_test_accuracy, atol=0.0001) + if True: + symbolic_weights = hard_weights # utils.make_symbolic(hard_weights) + symbolic_trained_state = train_state.TrainState.create( + apply_fn=symbolic.apply, params=symbolic_weights, tx=optax.sgd(1.0, 1.0) + ) + symbolic_input = hard_input.tolist() + symbolic_test_accuracy = apply_hard_model( + symbolic_trained_state, symbolic_input, y_test + ) + print( + "symbolic_net: final test_accuracy: %.2f" % (symbolic_test_accuracy * 100) + ) + assert numpy.isclose(test_accuracy, symbolic_test_accuracy, atol=0.0001) + if False: + # CPU and GPU give different results, so we can't easily regress on a static symbolic expression + symbolic_input = [f"x{i}" for i in range(len(hard_input[0].tolist()))] + symbolic_output = symbolic.apply({"params": symbolic_weights}, symbolic_input) + print("symbolic_output", symbolic_output[0][:10000]) + + +binary_iris = True +num_features = 16 if binary_iris else 4 +num_classes = 3 + + +def get_iris_data(): + data_dir = Path(__file__).parent.parent / "tests" / "data" + data = numpy.loadtxt( + data_dir / "iris.data", + delimiter=",", + dtype={ + "names": ( + "sepal_length", + "sepal_width", + "petal_length", + "petal_width", + "class", + ), + "formats": ("f4", "f4", "f4", "f4", "U15"), + }, + ) + features = numpy.array([list(d)[:4] for d in data]) + # Normalise each feature column to be in the range [0, 1] + features = (features - features.min(axis=0)) / ( + features.max(axis=0) - features.min(axis=0) + ) + labels = numpy.array( + [ + 0 + if d[num_features] == "Iris-setosa" + else 1 + if d[num_features] == "Iris-versicolor" + else 2 + for d in data + ] + ) + return features, labels + + +def get_binary_iris_data(): + data_dir = Path(__file__).parent.parent / "tests" / "data" + data = numpy.loadtxt(data_dir / "BinaryIrisData.txt").astype(dtype=numpy.int32) + features = data[:, 0:num_features] # Input features + labels = data[:, num_features] # Target value + return features, labels + + +# overfitting model: 100% training accuracy +def nln_iris(type, x, training: bool): + input_size = x.shape[0] + bits_per_feature = 10 + x = real_encoder.real_encoder_layer(type)(bits_per_feature)(x) + x = x.ravel() + dtype = jax.numpy.float32 + mask_layer_size = 120 + x = hard_masks.mask_to_true_margin_layer(type)(mask_layer_size, dtype=dtype)(x) + x = x.reshape((mask_layer_size, input_size * bits_per_feature)) + x = hard_majority.majority_layer(type)()(x) + x = hard_not.not_layer(type)(18)(x) + x = x.ravel() + ######################################################## + x = harden_layer.harden_layer(type)(x) + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = x.sum(-1) + return x + + +""" +| Technique/Accuracy | Mean | 5 %ile | 95 %ile | Min | Max | +| ------------------ | -------------- | ------- | ------- | ------ | ------ | +| Tsetlin | 95.0 +/- 0.2 | 86.7 | 100.0 | 80.0 | 100.0 | +| dB | 94.2 +/- 0.1 | 86.7 | 100.0 | 80.0 | 100.0 | +| Neural network | 93.8 +/- 0.2 | 86.7 | 100.0 | 80.0 | 100.0 | +| SVM | 93.6 +/- 0.3 | 86.7 | 100.0 | 76.7 | 100.0 | +| Naive Bayes | 91.6 +/- 0.3 | 83.3 | 96.7 | 70.0 | 100.0 | + +Source: https://arxiv.org/pdf/1804.01508.pdf +""" +# Using majority without margin +# mean: 94.18, sem: 0.13, min: 80.00, max: 100.00, 5%: 86.67, 95%: 100.00 +# Using majority with margin +# mean: 93.95, sem: 0.13, min: 76.67, max: 100.00, 5%: 86.67, 95%: 100.00 +def nln_binary_iris_1(type, x, training: bool): + dtype = jax.numpy.float32 + x = hard_masks.mask_to_true_layer(type)(120, dtype=dtype)(x) + x = hard_majority.majority_layer(type)()(x) + x = hard_dropout.hard_dropout(type)( + rate=0.25, + dropout_value=0.0, + deterministic=not training, + dtype=dtype, + )(x) + ######################################################## + x = harden_layer.harden_layer(type)(x) + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = x.sum(-1) + return x + +""" +| Technique/Accuracy | Mean | 5 %ile | 95 %ile | Min | Max | +| ------------------ | -------------- | ------- | ------- | ------ | ------ | +| Tsetlin | 95.0 +/- 0.2 | 86.7 | 100.0 | 80.0 | 100.0 | +| dB | 93.9 +/- 0.1 | 86.7 | 100.0 | 80.0 | 100.0 | +| Neural network | 93.8 +/- 0.2 | 86.7 | 100.0 | 80.0 | 100.0 | +| SVM | 93.6 +/- 0.3 | 86.7 | 100.0 | 76.7 | 100.0 | +| Naive Bayes | 91.6 +/- 0.3 | 83.3 | 96.7 | 70.0 | 100.0 | + +Source: https://arxiv.org/pdf/1804.01508.pdf +""" +# mean: 93.89, sem: 0.12, min: 80.00, max: 100.00, 5%: 86.67, 95%: 100.00 +# If we use margin-packing for hard_count then: +# mean: 93.80, sem: 0.13, min: 70.00, max: 100.00, 5%: 86.67, 95%: 100.00 +# If we use margin-packing for hard_count but without dropout and layer_size = 29 then: +# mean: 93.76, sem: 0.13, min: 73.33, max: 100.00, 5%: 86.67, 95%: 100.00 +def nln_binary_iris(type, x, training: bool): + dtype = jax.numpy.float64 + y = hard_vmap.vmap(type)((lambda x: 1 - x, lambda x: 1 - x, lambda x: symbolic_primitives.symbolic_not(x)))(x) + x = hard_concatenate.concatenate(type)([x, y], 0) + layer_size = 59 + x = hard_and.and_layer(type)( + layer_size, + dtype=dtype, + weights_init=initialization.initialize_uniform_range(0.49, 0.49), + )(x) + x = hard_dropout.hard_dropout(type)( + rate=0.05, + dropout_function=lambda x: 1-x, + deterministic=not training, + dtype=dtype, + )(x) + ######################################################## + x = jax.numpy.array([x]) # TODO: shouldn't need to do this + # count the number of high bits to yield layer_size+1 outputs + x = hard_count.count_layer(type)()(x) + # split into num_classes equally sized bit buckets + x = x.ravel() # TODO: shouldn't need to do this + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + # take the logical or of each bucket + # TODO: create a specialised layer for this + x = hard_vmap.vmap(type)(( + lambda x: jax.numpy.max(x), + # This is conceptually wrong + #lambda x: hard_or.soft_or_vec(x), # I don't want the other bits in the bucket to be high (if correct label) + lambda x: jax.numpy.max(x), + lambda x: symbolic_primitives.symbolic_reduce_or(x)))(x) + x = x.ravel() + x = harden_layer.harden_layer(type)(x) + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) # TODO: shouldn't need to do this + x = x.sum(-1) + return x + + + +def batch_nln_iris(type, x, training: bool): + return jax.vmap(lambda x: nln_iris(type, x, training))(x) + + +def batch_nln_binary_iris(type, x, training: bool): + return jax.vmap(lambda x: nln_binary_iris(type, x, training))(x) + + +class TrainState(train_state.TrainState): + dropout_rng: jax.random.KeyArray + + +def create_train_state(net, rng, dropout_rng, config): + mock_input = jax.numpy.ones([1, num_features]) + soft_weights = net.init(rng, mock_input, training=False)["params"] + tx = optax.radam(learning_rate=config.learning_rate) + return TrainState.create( + apply_fn=net.apply, params=soft_weights, tx=tx, dropout_rng=dropout_rng + ) + + +@jax.jit +def update_model(state, grads): + return state.apply_gradients(grads=grads) + +def apply_model_with_grad_impl(state, features, labels, dropout_rng, training: bool): + dropout_train_rng = jax.random.fold_in(key=dropout_rng, data=state.step) + + def loss_fn(params): + logits = state.apply_fn( + {"params": params}, + features, + training=training, + rngs={"dropout": dropout_train_rng}, + ) + one_hot = jax.nn.one_hot(labels, num_classes) + loss = jax.numpy.mean( + optax.softmax_cross_entropy(logits=logits, labels=one_hot) + ) + return loss, logits + + grad_fn = jax.value_and_grad(loss_fn, has_aux=True) + (loss, logits), grads = grad_fn(state.params) + accuracy = jax.numpy.mean(jax.numpy.argmax(logits, -1) == labels) + return grads, loss, accuracy + + +@jax.jit +def apply_model_with_grad_and_training(state, features, labels, dropout_rng): + return apply_model_with_grad_impl( + state, features, labels, dropout_rng, training=True + ) + + +@jax.jit +def apply_model_with_grad(state, features, labels, dropout_rng): + return apply_model_with_grad_impl( + state, features, labels, dropout_rng, training=False + ) + + +def train_epoch(state, features, labels, batch_size, rng, dropout_rng): + train_ds_size = len(features) + steps_per_epoch = train_ds_size // batch_size + + perms = jax.random.permutation(rng, len(features)) + perms = perms[: steps_per_epoch * batch_size] # skip incomplete batch + perms = perms.reshape((steps_per_epoch, batch_size)) + + epoch_loss = [] + epoch_accuracy = [] + + for perm in perms: + batch_features = features[perm, ...] + batch_labels = labels[perm, ...] + grads, loss, accuracy = apply_model_with_grad_and_training( + state, batch_features, batch_labels, dropout_rng + ) + state = update_model(state, grads) + epoch_loss.append(loss) + epoch_accuracy.append(accuracy) + train_loss = numpy.mean(epoch_loss) + train_accuracy = numpy.mean(epoch_accuracy) + return state, train_loss, train_accuracy + + +def train_and_evaluate( + init_rng, dropout_rng, net, data, config: ml_collections.ConfigDict +): + state = create_train_state(net, init_rng, dropout_rng, config) + x_training, y_training, x_test, y_test = data + best_train_accuracy = 0.0 + best_test_accuracy = 0.0 + for epoch in range(1, config.num_epochs + 1): + init_rng, input_rng = jax.random.split(init_rng) + state, train_loss, train_accuracy = train_epoch( + state, x_training, y_training, config.batch_size, input_rng, dropout_rng + ) + _, test_loss, test_accuracy = apply_model_with_grad( + state, x_test, y_test, dropout_rng + ) + if train_accuracy > best_train_accuracy: + best_train_accuracy = train_accuracy + # print(f"epoch: {epoch}") + # print(f"\tbest_train_accuracy: {best_train_accuracy * 100:.2f}") + if test_accuracy >= best_test_accuracy: + best_test_accuracy = test_accuracy + # print(f"\tbest_test_accuracy: {best_test_accuracy * 100:.2f}") + # else: + # print(f"\ttest_accuracy: {test_accuracy * 100:.2f}") + # print("\n") + + print( + "epoch:% 3d, train_loss: %.4f, train_accuracy: %.2f, test_loss: %.4f, test_accuracy: %.2f" + % (epoch, train_loss, train_accuracy * 100, test_loss, test_accuracy * 100) + ) + + # return trained state and final test_accuracy + return state, test_accuracy + + +def apply_hard_model(state, features, label): + def logits_fn(params): + return state.apply_fn({"params": params}, features, training=False) + + logits = logits_fn(state.params) + if isinstance(logits, list): + logits = jax.numpy.array(logits) + logits *= 1.0 + accuracy = jax.numpy.mean(jax.numpy.argmax(logits, -1) == label) + return accuracy + + +def apply_hard_model_to_data(state, features, labels): + accuracy = 0 + for image, label in tqdm(zip(features, labels), total=len(features)): + accuracy += apply_hard_model(state, image, label) + return accuracy / len(features) + + +def get_config(): + config = ml_collections.ConfigDict() + config.learning_rate = 0.01 # sgd = 0.1 + config.momentum = 0.9 + config.batch_size = 60 + config.num_epochs = 1000 + return config + + +def train_test_split(features, labels, rng, test_size=0.2): + rng, split_rng = jax.random.split(rng) + train_size = int(len(features) * (1 - test_size)) + train_idx = jax.random.permutation(split_rng, len(features))[:train_size] + test_idx = jax.random.permutation(split_rng, len(features))[train_size:] + return ( + features[train_idx], + features[test_idx], + labels[train_idx], + labels[test_idx], + ) + +@pytest.mark.skip(reason="temporarily off") +def test_iris(): + # Train net + if binary_iris: + features, labels = get_binary_iris_data() + soft, hard, symbolic = neural_logic_net.net( + lambda type, x, training: batch_nln_binary_iris(type, x, training) + ) + else: + features, labels = get_iris_data() + soft, hard, symbolic = neural_logic_net.net( + lambda type, x, training: batch_nln_iris(type, x, training) + ) + + rng = jax.random.PRNGKey(0) + print(soft.tabulate(rng, features[0:1], training=False)) + + num_experiments = 1000 # 1000 for paper + final_test_accuracies = [] + for i in range(num_experiments): + # Split features and labels into 80% training and 20% test + rng, int_rng, dropout_rng = jax.random.split(rng, 3) + x_training, x_test, y_training, y_test = train_test_split( + features, labels, rng, test_size=0.2 + ) + trained_state, final_test_accuracy = train_and_evaluate( + int_rng, + dropout_rng, + soft, + (x_training, y_training, x_test, y_test), + get_config(), + ) + final_test_accuracies.append(final_test_accuracy) + print(f"{i}: final test accuracy: {final_test_accuracy * 100:.2f}") + # print mean, standard error of the mean, min, max, lowest 5%, highest 5% of final test accuracies + print( + f"mean: {numpy.mean(final_test_accuracies) * 100:.2f}, " + f"sem: {scipy.stats.sem(final_test_accuracies) * 100:.2f}, " + f"min: {numpy.min(final_test_accuracies) * 100:.2f}, " + f"max: {numpy.max(final_test_accuracies) * 100:.2f}, " + f"5%: {numpy.percentile(final_test_accuracies, 5) * 100:.2f}, " + f"95%: {numpy.percentile(final_test_accuracies, 95) * 100:.2f}" + ) + + # Check symbolic net + # _, hard, symbolic = neural_logic_net.net(lambda type, x: nln(type, x)) + # check_symbolic((soft, hard, symbolic), (x_training, y_training, x_test, y_test), trained_state) diff --git a/tests/test_mnist.py b/tests/test_mnist.py index b2803cd..93ec7d9 100644 --- a/tests/test_mnist.py +++ b/tests/test_mnist.py @@ -7,63 +7,31 @@ import tensorflow as tf import tensorflow_datasets as tfds from flax import linen as nn -from flax.metrics import tensorboard from flax.training import train_state from jax.config import config -from matplotlib import pyplot as plt from tqdm import tqdm -from neurallogic import (hard_and, hard_majority, hard_not, hard_or, harden, - harden_layer, neural_logic_net, real_encoder) +from neurallogic import ( + hard_and, + hard_majority, + hard_not, + hard_or, + hard_xor, + hard_masks, + harden, + harden_layer, + neural_logic_net, + real_encoder, + hard_dropout, + initialization, + hard_count, + hard_vmap, + symbolic_primitives, + hard_concatenate +) # Uncomment to debug NaNs -#config.update("jax_debug_nans", True) - -""" -MNIST test. - -Executes the training and evaluation loop for MNIST. -The data is loaded using tensorflow_datasets. -""" - -# TODO: experiment in ipython notebook with different values for these -""" -def nln(type, x, width): - #x = x.reshape((-1, 1)) - #re = real_encoder.real_encoder_layer(type)(3) - #x = jax.vmap(re, 0)(x) - #x = x.ravel() - #x = hard_or.or_layer(type)(width, nn.initializers.uniform(1.0), dtype=jax.numpy.float16)(x) - x = hard_or.or_layer(type)(width, nn.initializers.uniform(1.0), dtype=jax.numpy.float16)(x) - x = hard_not.not_layer(type)(10)(x) - x = x.ravel() # flatten the outputs of the not layer - # harden the outputs of the not layer - x = harden_layer.harden_layer(type)(x) - x = x.reshape((10, width)) # reshape to 10 ports, 100 bits each - x = x.sum(-1) # sum the 100 bits in each port - return x -""" - -def nln(type, x, width): - my_width = 600 - not_size = 5 - #majority_size = 3 - num_classes = 10 - - x = hard_or.or_layer(type)(my_width, nn.initializers.uniform(1.0), dtype=jax.numpy.float16)(x) # width number of or neurons - x = hard_and.and_layer(type)(int(my_width), dtype=jax.numpy.float16)(x) - x = hard_not.not_layer(type)(not_size, dtype=jax.numpy.float16)(x) - x = x.ravel() - #x = x.reshape((int(width * not_size / majority_size), majority_size)) - #x = hard_majority.majority_layer(type)(x) - x = harden_layer.harden_layer(type)(x) - x = x.reshape((num_classes, int(x.shape[0] / num_classes))) - x = x.sum(-1) - return x - - -def batch_nln(type, x, width): - return jax.vmap(lambda x: nln(type, x, width))(x) +# config.update("jax_debug_nans", True) class CNN(nn.Module): @@ -84,12 +52,98 @@ def __call__(self, x): return x -@jax.jit -def apply_model_with_grad(state, images, labels): - """Computes gradients, loss and accuracy for a single batch.""" +def check_symbolic(nets, datasets, trained_state, dropout_rng): + _, test_ds = datasets + _, hard, symbolic = nets + _, test_loss, test_accuracy = apply_model_with_grad( + trained_state, test_ds["image"], test_ds["label"], dropout_rng + ) + print( + "soft_net: final test_loss: %.4f, final test_accuracy: %.2f" + % (test_loss, test_accuracy * 100) + ) + hard_weights = harden.hard_weights(trained_state.params) + hard_trained_state = train_state.TrainState.create( + apply_fn=hard.apply, params=hard_weights, tx=optax.sgd(1.0, 1.0) + ) + hard_input = harden.harden(test_ds["image"]) + hard_test_accuracy = apply_hard_model_to_images( + hard_trained_state, hard_input, test_ds["label"] + ) + print("hard_net: final test_accuracy: %.2f" % (hard_test_accuracy * 100)) + assert np.isclose(test_accuracy, hard_test_accuracy, atol=0.0001) + # TODO: activate these checks + if False: + # It takes too long to compute this + symbolic_weights = harden.symbolic_weights(trained_state.params) + symbolic_trained_state = train_state.TrainState.create( + apply_fn=symbolic.apply, params=symbolic_weights, tx=optax.sgd(1.0, 1.0) + ) + symbolic_input = hard_input.tolist() + symbolic_test_accuracy = apply_hard_model_to_images( + symbolic_trained_state, symbolic_input, test_ds["label"] + ) + print( + "symbolic_net: final test_accuracy: %.2f" % (symbolic_test_accuracy * 100) + ) + assert np.isclose(test_accuracy, symbolic_test_accuracy, atol=0.0001) + if False: + # CPU and GPU give different results, so we can't easily regress on a static symbolic expression + symbolic_input = [f"x{i}" for i in range(len(hard_input[0].tolist()))] + symbolic_output = symbolic.apply({"params": symbolic_weights}, symbolic_input) + print("symbolic_output", symbolic_output[0][:10000]) + + +# about 95% training, 93-4% test +# batch size 6000 +def nln_1(type, x, training: bool): + input_size = 784 + mask_layer_size = 60 + dtype = jax.numpy.float32 + x = hard_masks.mask_to_true_layer(type)(mask_layer_size, dtype=dtype, + weights_init=initialization.initialize_bernoulli(0.01, 0.3, 0.501))(x) + x = x.reshape((2940, 16)) + x = hard_majority.majority_layer(type)()(x) + x = hard_not.not_layer(type)(20, weights_init=nn.initializers.uniform(1.0), dtype=dtype)(x) + x = x.ravel() + ############################## + x = harden_layer.harden_layer(type)(x) + num_classes = 10 + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = x.sum(-1) + return x + +def nln(type, x, training: bool): + input_size = 784 + mask_layer_size = 200 + dtype = jax.numpy.float32 + x = hard_masks.mask_to_true_layer(type)(mask_layer_size, dtype=dtype, + weights_init=initialization.initialize_bernoulli(0.01, 0.3, 0.501))(x) + x = x.reshape((9800, 16)) + x = hard_majority.majority_layer(type)()(x) + x = hard_not.not_layer(type)(20, weights_init=nn.initializers.uniform(1.0), dtype=dtype)(x) + x = x.ravel() + ############################## + x = harden_layer.harden_layer(type)(x) + num_classes = 10 + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = x.sum(-1) + return x + +def batch_nln(type, x, training: bool): + return jax.vmap(lambda x: nln(type, x, training))(x) + + +def apply_model_with_grad_impl(state, images, labels, dropout_rng, training: bool): + dropout_train_rng = jax.random.fold_in(key=dropout_rng, data=state.step) def loss_fn(params): - logits = state.apply_fn({"params": params}, images) + logits = state.apply_fn( + {"params": params}, + images, + training=training, + rngs={"dropout": dropout_train_rng}, + ) one_hot = jax.nn.one_hot(labels, 10) loss = jnp.mean(optax.softmax_cross_entropy(logits=logits, labels=one_hot)) return loss, logits @@ -100,12 +154,24 @@ def loss_fn(params): return grads, loss, accuracy +@jax.jit +def apply_model_with_grad_and_training(state, images, labels, dropout_rng): + return apply_model_with_grad_impl(state, images, labels, dropout_rng, training=True) + + +@jax.jit +def apply_model_with_grad(state, images, labels, dropout_rng): + return apply_model_with_grad_impl( + state, images, labels, dropout_rng, training=False + ) + + @jax.jit def update_model(state, grads): return state.apply_gradients(grads=grads) -def train_epoch(state, train_ds, batch_size, rng): +def train_epoch(state, train_ds, batch_size, rng, dropout_rng): """Train for a single epoch.""" train_ds_size = len(train_ds["image"]) steps_per_epoch = train_ds_size // batch_size @@ -120,7 +186,9 @@ def train_epoch(state, train_ds, batch_size, rng): for perm in perms: batch_images = train_ds["image"][perm, ...] batch_labels = train_ds["label"][perm, ...] - grads, loss, accuracy = apply_model_with_grad(state, batch_images, batch_labels) + grads, loss, accuracy = apply_model_with_grad_and_training( + state, batch_images, batch_labels, dropout_rng + ) state = update_model(state, grads) epoch_loss.append(loss) epoch_accuracy.append(accuracy) @@ -136,16 +204,18 @@ def get_datasets(): test_ds = tfds.as_numpy(ds_builder.as_dataset(split="test", batch_size=-1)) train_ds["image"] = jnp.float32(train_ds["image"]) / 255.0 test_ds["image"] = jnp.float32(test_ds["image"]) / 255.0 - # TODO: we don't need to do this even when we don't use the real encoder - # Use grayscale information # Convert the floating point values in [0,1] to binary values in {0,1} - train_ds["image"] = jnp.round(train_ds["image"]) - test_ds["image"] = jnp.round(test_ds["image"]) + # If the float value is > 0.3 then we convert to 1, otherwise 0 + train_ds["image"] = jnp.where(train_ds["image"] > 0.3, 1.0, 0.0) + test_ds["image"] = jnp.where(test_ds["image"] > 0.3, 1.0, 0.0) + #train_ds["image"] = jnp.round(train_ds["image"]) + #test_ds["image"] = jnp.round(test_ds["image"]) return train_ds, test_ds def show_img(img, ax=None, title=None): """Shows a single image.""" + """ if ax is None: ax = plt.gca() ax.imshow(img.reshape(28, 28), cmap="gray") @@ -153,55 +223,50 @@ def show_img(img, ax=None, title=None): ax.set_yticks([]) if title: ax.set_title(title) - + """ def show_img_grid(imgs, titles): """Shows a grid of images.""" + """ n = int(np.ceil(len(imgs) ** 0.5)) _, axs = plt.subplots(n, n, figsize=(3 * n, 3 * n)) for i, (img, title) in enumerate(zip(imgs, titles)): show_img(img, axs[i // n][i % n], title) + """ + +class TrainState(train_state.TrainState): + dropout_rng: jax.random.KeyArray -def create_train_state(net, rng, config): - """Creates initial `TrainState`.""" - # for CNN - # mock_input = jnp.ones([1, 28, 28, 1]) - # for NLN +def create_train_state(net, rng, dropout_rng, config): + # for CNN: mock_input = jnp.ones([1, 28, 28, 1]) mock_input = jnp.ones([1, 28 * 28]) - soft_weights = net.init(rng, mock_input)["params"] - #tx = optax.sgd(config.learning_rate, config.momentum) - #tx = optax.noisy_sgd(config.learning_rate, config.momentum) - tx = optax.yogi(config.learning_rate) - return train_state.TrainState.create(apply_fn=net.apply, params=soft_weights, tx=tx) + soft_weights = net.init(rng, mock_input, training=False)["params"] + # tx = optax.yogi(config.learning_rate) # for nln_2 + tx = optax.radam(config.learning_rate) + return TrainState.create( + apply_fn=net.apply, params=soft_weights, tx=tx, dropout_rng=dropout_rng + ) def train_and_evaluate( - net, datasets, config: ml_collections.ConfigDict, workdir: str -) -> train_state.TrainState: - """Execute model training and evaluation loop. - Args: - config: Hyperparameter configuration for training and evaluation. - workdir: Directory where the tensorboard summaries are written to. - Returns: - The train state (which includes the `.params`). - """ - train_ds, test_ds = datasets - rng = jax.random.PRNGKey(0) - - summary_writer = tensorboard.SummaryWriter(workdir) - summary_writer.hparams(dict(config)) - - rng, init_rng = jax.random.split(rng) - state = create_train_state(net, init_rng, config) + init_rng, + dropout_rng, + net, + datasets, + config: ml_collections.ConfigDict, + workdir: str, +): + state = create_train_state(net, init_rng, dropout_rng, config) + train_dataset, test_dataset = datasets for epoch in range(1, config.num_epochs + 1): - rng, input_rng = jax.random.split(rng) + init_rng, input_rng = jax.random.split(init_rng) state, train_loss, train_accuracy = train_epoch( - state, train_ds, config.batch_size, input_rng + state, train_dataset, config.batch_size, input_rng, dropout_rng ) _, test_loss, test_accuracy = apply_model_with_grad( - state, test_ds["image"], test_ds["label"] + state, test_dataset["image"], test_dataset["label"], dropout_rng ) print( @@ -209,32 +274,9 @@ def train_and_evaluate( % (epoch, train_loss, train_accuracy * 100, test_loss, test_accuracy * 100) ) - summary_writer.scalar("train_loss", train_loss, epoch) - summary_writer.scalar("train_accuracy", train_accuracy, epoch) - summary_writer.scalar("test_loss", test_loss, epoch) - summary_writer.scalar("test_accuracy", test_accuracy, epoch) - return state -def get_config(): - """Get the default hyperparameter configuration.""" - config = ml_collections.ConfigDict() - - # config for CNN - config.learning_rate = 0.01 - # config for NLN - #config.learning_rate = 0.1 - config.learning_rate = 0.01 - - # Always commit with num_epochs = 1 for short test time - config.momentum = 0.9 - config.batch_size = 128 - #config.num_epochs = 2 - config.num_epochs = 1000 - return config - - def apply_hard_model(state, image, label): def logits_fn(params): return state.apply_fn({"params": params}, image) @@ -254,75 +296,51 @@ def apply_hard_model_to_images(state, images, labels): return accuracy / len(images) -def check_symbolic(nets, datasets, trained_state): - _, test_ds = datasets - _, hard, symbolic = nets - _, test_loss, test_accuracy = apply_model_with_grad( - trained_state, test_ds["image"], test_ds["label"] - ) - print( - "soft_net: final test_loss: %.4f, final test_accuracy: %.2f" - % (test_loss, test_accuracy * 100) - ) - hard_weights = harden.hard_weights(trained_state.params) - hard_trained_state = train_state.TrainState.create( - apply_fn=hard.apply, params=hard_weights, tx=optax.sgd(1.0, 1.0) - ) - hard_input = harden.harden(test_ds["image"]) - hard_test_accuracy = apply_hard_model_to_images( - hard_trained_state, hard_input, test_ds["label"] - ) - print("hard_net: final test_accuracy: %.2f" % (hard_test_accuracy * 100)) - assert np.isclose(test_accuracy, hard_test_accuracy, atol=0.0001) - # TODO: activate these checks - if False: - # It takes too long to compute this - symbolic_weights = harden.symbolic_weights(trained_state.params) - symbolic_trained_state = train_state.TrainState.create( - apply_fn=symbolic.apply, params=symbolic_weights, tx=optax.sgd(1.0, 1.0) - ) - symbolic_input = hard_input.tolist() - symbolic_test_accuracy = apply_hard_model_to_images( - symbolic_trained_state, symbolic_input, test_ds["label"] - ) - print( - "symbolic_net: final test_accuracy: %.2f" % (symbolic_test_accuracy * 100) - ) - assert np.isclose(test_accuracy, symbolic_test_accuracy, atol=0.0001) - if False: - # CPU and GPU give different results, so we can't easily regress on a static symbolic expression - symbolic_input = [f"x{i}" for i in range(len(hard_input[0].tolist()))] - symbolic_output = symbolic.apply({"params": symbolic_weights}, symbolic_input) - print("symbolic_output", symbolic_output[0][:10000]) +def get_config(): + config = ml_collections.ConfigDict() + # config for CNN: config.learning_rate = 0.01 + config.learning_rate = 0.01 + config.momentum = 0.9 + config.batch_size = 3000 # 6000 # 128 + config.num_epochs = 5000 + return config + @pytest.mark.skip(reason="temporarily off") def test_mnist(): # Make sure tf does not allocate gpu memory. tf.config.experimental.set_visible_devices([], "GPU") - # Define training configuration. - config = get_config() + rng = jax.random.PRNGKey(0) + rng, int_rng, dropout_rng = jax.random.split(rng, 3) - # Define the model. # soft = CNN() - width = 800 - soft, hard, _ = neural_logic_net.net(lambda type, x: batch_nln(type, x, width)) + soft, _, _ = neural_logic_net.net( + lambda type, x, training: batch_nln(type, x, training) + ) - # Get the MNIST dataset. train_ds, test_ds = get_datasets() # If we're using a NLN then flatten the images train_ds["image"] = jnp.reshape(train_ds["image"], (train_ds["image"].shape[0], -1)) test_ds["image"] = jnp.reshape(test_ds["image"], (test_ds["image"].shape[0], -1)) - print(soft.tabulate(jax.random.PRNGKey(0), train_ds["image"][0:1])) - # TODO: fix the size of this - #print(hard.tabulate(jax.random.PRNGKey(0), harden.harden(train_ds["image"][0:1]))) + print(soft.tabulate(rng, train_ds["image"][0:1], training=False)) + + # TODO: 50 experiments # Train and evaluate the model. trained_state = train_and_evaluate( - soft, (train_ds, test_ds), config=config, workdir="./mnist_metrics" + int_rng, + dropout_rng, + soft, + (train_ds, test_ds), + config=get_config(), + workdir="./mnist_metrics", ) # Check symbolic net - #_, hard, symbolic = neural_logic_net.net(lambda type, x: nln(type, x, width)) - #check_symbolic((soft, hard, symbolic), (train_ds, test_ds), trained_state) + #_, hard, symbolic = neural_logic_net.net(lambda type, x: nln(type, x, False)) + #check_symbolic( + # (soft, hard, symbolic), (train_ds, test_ds), trained_state, dropout_rng + #) + diff --git a/tests/test_network.py b/tests/test_network.py index 751fd09..fe153d3 100644 --- a/tests/test_network.py +++ b/tests/test_network.py @@ -20,7 +20,7 @@ def test_net(type, x): 16, nn.initializers.uniform(1.0), jnp.float64)(x) x = hard_and.and_layer(type)( 4, nn.initializers.uniform(1.0), jnp.float64)(x) - x = hard_not.not_layer(type)(1, dtype=jnp.float64)(x) + x = hard_not.not_layer(type)(1, weights_init=nn.initializers.uniform(1.0), dtype=jnp.float64)(x) x = x.ravel() x = harden_layer.harden_layer(type)(x) return x @@ -43,7 +43,7 @@ def test_net(type, x): output = jnp.array(y) # Train the and layer - tx = optax.sgd(0.01) + tx = optax.sgd(0.1) state = train_state.TrainState.create(apply_fn=jax.vmap( soft.apply, in_axes=(None, 0)), params=soft_weights, tx=tx) grad_fn = jax.jit(jax.value_and_grad(lambda params, x, diff --git a/tests/test_noisy_xor.py b/tests/test_noisy_xor.py new file mode 100644 index 0000000..98ff09a --- /dev/null +++ b/tests/test_noisy_xor.py @@ -0,0 +1,333 @@ +import sys +from pathlib import Path + +import jax +import ml_collections +import numpy +import optax +import scipy +from flax import linen as nn +from flax.training import train_state +from jax.config import config +from tqdm import tqdm + +from neurallogic import ( + hard_and, + hard_majority, + hard_not, + hard_or, + harden, + harden_layer, + neural_logic_net, + initialization, + symbolic_primitives, + hard_vmap, + hard_concatenate +) +from tests import utils + +config.update("jax_enable_x64", True) + +def check_symbolic(nets, data, trained_state, dropout_rng): + x_training, y_training, x_test, y_test = data + _, hard, symbolic = nets + _, test_loss, test_accuracy = apply_model_with_grad( + trained_state, x_test, y_test, dropout_rng + ) + print( + "soft_net: final test_loss: %.4f, final test_accuracy: %.2f" + % (test_loss, test_accuracy * 100) + ) + hard_weights = harden.hard_weights(trained_state.params) + hard_trained_state = TrainState.create( + apply_fn=hard.apply, + params=hard_weights, + tx=optax.sgd(1.0, 1.0), + dropout_rng=dropout_rng, + ) + hard_input = harden.harden(x_test) + hard_test_accuracy = apply_hard_model_to_data( + hard_trained_state, hard_input, y_test + ) + print("hard_net: final test_accuracy: %.2f" % (hard_test_accuracy * 100)) + assert numpy.isclose(test_accuracy, hard_test_accuracy, atol=0.0001) + + if False: + symbolic_weights = hard_weights # utils.make_symbolic(hard_weights) + symbolic_trained_state = train_state.TrainState.create( + apply_fn=symbolic.apply, + params=symbolic_weights, + tx=optax.sgd(1.0, 1.0), + dropout_rng=dropout_rng, + ) + symbolic_input = hard_input.tolist() + symbolic_test_accuracy = apply_hard_model( + symbolic_trained_state, symbolic_input, y_test + ) + print( + "symbolic_net: final test_accuracy: %.2f" % (symbolic_test_accuracy * 100) + ) + assert numpy.isclose(test_accuracy, symbolic_test_accuracy, atol=0.0001) + if True: + # CPU and GPU give different results, so we can't easily regress on a static symbolic expression + symbolic_input = [f"x{i}" for i in range(len(hard_input[0].tolist()))] + # This simply checks that the symbolic output can be generated + symbolic_output = symbolic.apply({"params": hard_weights}, symbolic_input, training=False) + +num_features = 12 +num_classes = 2 + + +def get_data(): + # Create a path to the data directory + data_dir = Path(__file__).parent.parent / "tests" / "data" + # Load the training data + training_data = numpy.loadtxt(data_dir / "NoisyXORTrainingData.txt").astype( + dtype=numpy.float32 + ) + # Load the test data + test_data = numpy.loadtxt(data_dir / "NoisyXORTestData.txt").astype( + dtype=numpy.float32 + ) + return training_data, test_data + + +""" +| Technique/Accuracy | Mean | 5 %ile | 95 %ile | Min | Max | +| ------------------- | -------------- | ------- | ------- | ------ | ------ | +| Tsetlin | 99.3 +/- 0.3 | 95.9 | 100.0 | 91.6 | 100.0 | +| dB | 97.9 +/- 0.2 | 95.4 | 100.0 | 93.6 | 100.0 | +| Neural network | 95.4 +/- 0.5 | 90.1 | 98.6 | 88.2 | 99.9 | +| SVM | 58.0 +/- 0.3 | 56.4 | 59.2 | 55.4 | 66.5 | +| Naive Bayes | 49.8 +/- 0.2 | 48.3 | 51.0 | 41.3 | 52.7 | +| Logistic regression | 49.8 +/- 0.3 | 47.8 | 51.1 | 41.1 | 53.1 | + +Source: https://arxiv.org/pdf/1804.01508.pdf +""" +# N.B. We use marginal versions of and/or layers for this performance +# mean: 97.89, sem: 0.15, min: 93.58, max: 100.00, 5%: 95.40, 95%: 100.00 +def nln(type, x, training: bool): + y = hard_vmap.vmap(type)((lambda x: 1 - x, lambda x: 1 - x, lambda x: symbolic_primitives.symbolic_not(x)))(x) + x = hard_concatenate.concatenate(type)([x, y], 0) + + layer_size = 32 + dtype = jax.numpy.float64 + x = hard_and.and_layer(type)( + layer_size, + dtype=dtype, + weights_init=initialization.initialize_bernoulli(0.01, 0.3, 0.501), + )(x) + x = hard_or.or_layer(type)( + layer_size, + dtype=dtype, + weights_init=initialization.initialize_bernoulli(0.99, 0.499, 0.7), + )(x) + not_layer_size = 16 + x = hard_not.not_layer(type)( + not_layer_size, + dtype=dtype, + weights_init=initialization.initialize_uniform_range(0.499, 0.501), + )(x) + + x = x.reshape((1, layer_size * not_layer_size)) + x = hard_majority.majority_layer(type)()(x) + + z = hard_vmap.vmap(type)((lambda x: 1 - x, lambda x: 1 - x, lambda x: symbolic_primitives.symbolic_not(x)))(x) + x = hard_concatenate.concatenate(type)([x, z], 0) + + ######################################################## + + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = x.sum(-1) + return x + + +def batch_nln(type, x, training: bool): + return jax.vmap(lambda x: nln(type, x, training))(x) + + +class TrainState(train_state.TrainState): + dropout_rng: jax.random.KeyArray + + +def create_train_state(net, rng, dropout_rng, config): + mock_input = jax.numpy.ones([1, num_features]) + soft_weights = net.init(rng, mock_input, training=False)["params"] + tx = optax.radam(learning_rate=config.learning_rate) + return TrainState.create( + apply_fn=net.apply, params=soft_weights, tx=tx, dropout_rng=dropout_rng + ) + + +@jax.jit +def update_model(state, grads): + return state.apply_gradients(grads=grads) + + +def apply_model_with_grad_impl(state, features, labels, dropout_rng, training: bool): + dropout_train_rng = jax.random.fold_in(key=dropout_rng, data=state.step) + + def loss_fn(params): + logits = state.apply_fn( + {"params": params}, + features, + training=training, + rngs={"dropout": dropout_train_rng}, + ) + one_hot = jax.nn.one_hot(labels, num_classes, dtype=jax.numpy.int32) + loss = jax.numpy.mean( + optax.softmax_cross_entropy(logits=logits, labels=one_hot) + ) + return loss, logits + + grad_fn = jax.value_and_grad(loss_fn, has_aux=True) + (loss, logits), grads = grad_fn(state.params) + accuracy = jax.numpy.mean(jax.numpy.argmax(logits, -1) == labels) + return grads, loss, accuracy + + +@jax.jit +def apply_model_with_grad_and_training(state, features, labels, dropout_rng): + return apply_model_with_grad_impl( + state, features, labels, dropout_rng, training=True + ) + + +@jax.jit +def apply_model_with_grad(state, features, labels, dropout_rng): + return apply_model_with_grad_impl( + state, features, labels, dropout_rng, training=False + ) + + +def train_epoch(state, features, labels, batch_size, rng, dropout_rng): + train_ds_size = len(features) + steps_per_epoch = train_ds_size // batch_size + + perms = jax.random.permutation(rng, len(features)) + perms = perms[: steps_per_epoch * batch_size] # skip incomplete batch + perms = perms.reshape((steps_per_epoch, batch_size)) + + epoch_loss = [] + epoch_accuracy = [] + + for perm in perms: + batch_features = features[perm, ...] + batch_labels = labels[perm, ...] + grads, loss, accuracy = apply_model_with_grad_and_training( + state, batch_features, batch_labels, dropout_rng + ) + state = update_model(state, grads) + epoch_loss.append(loss) + epoch_accuracy.append(accuracy) + train_loss = numpy.mean(epoch_loss) + train_accuracy = numpy.mean(epoch_accuracy) + return state, train_loss, train_accuracy + + +def get_train_and_test_data(data): + training_data, test_data = data + x_training = training_data[:, 0:num_features] # Input features + y_training = training_data[:, num_features] # Target value + x_test = test_data[:, 0:num_features] # Input features + y_test = test_data[:, num_features] # Target value + return x_training, y_training, x_test, y_test + + +def train_and_evaluate( + init_rng, dropout_rng, net, data, config: ml_collections.ConfigDict +): + state = create_train_state(net, init_rng, dropout_rng, config) + x_training, y_training, x_test, y_test = data + for epoch in range(1, config.num_epochs + 1): + init_rng, input_rng = jax.random.split(init_rng) + state, train_loss, train_accuracy = train_epoch( + state, x_training, y_training, config.batch_size, input_rng, dropout_rng + ) + _, test_loss, test_accuracy = apply_model_with_grad( + state, x_test, y_test, dropout_rng + ) + + print( + "epoch:% 3d, train_loss: %.4f, train_accuracy: %.2f, test_loss: %.4f, test_accuracy: %.2f" + % (epoch, train_loss, train_accuracy * 100, test_loss, test_accuracy * 100) + ) + + return state, test_accuracy + + +def apply_hard_model(state, features, label): + def logits_fn(params): + return state.apply_fn({"params": params}, features, training=False) + + logits = logits_fn(state.params) + if isinstance(logits, list): + logits = jax.numpy.array(logits) + logits *= 1.0 + accuracy = jax.numpy.mean(jax.numpy.argmax(logits, -1) == label) + return accuracy + + +def apply_hard_model_to_data(state, features, labels): + accuracy = 0 + for image, label in tqdm(zip(features, labels), total=len(features)): + accuracy += apply_hard_model(state, image, label) + return accuracy / len(features) + + +def get_config(): + config = ml_collections.ConfigDict() + config.learning_rate = 0.01 + config.batch_size = 5000 + config.num_epochs = 2000 # 2000 for paper + return config + + +def test_noisy_xor(): + # Train net + soft, _, _ = neural_logic_net.net( + lambda type, x, training: batch_nln(type, x, training) + ) + + x_training, y_training, x_test, y_test = get_train_and_test_data(get_data()) + + rng = jax.random.PRNGKey(0) + print(soft.tabulate(rng, x_training[0:1], training=False)) + + num_experiments = 1 # 100 for paper + final_test_accuracies = [] + for i in range(num_experiments): + rng, int_rng, dropout_rng = jax.random.split(rng, 3) + trained_state, final_test_accuracy = train_and_evaluate( + int_rng, + dropout_rng, + soft, + (x_training, y_training, x_test, y_test), + get_config(), + ) + final_test_accuracies.append(final_test_accuracy) + print(f"{i}: final test accuracy: {final_test_accuracy * 100:.2f}") + # print mean, standard error of the mean, min, max, lowest 5%, highest 5% of final test accuracies + print( + f"mean: {numpy.mean(final_test_accuracies) * 100:.2f}, " + f"sem: {scipy.stats.sem(final_test_accuracies) * 100:.2f}, " + f"min: {numpy.min(final_test_accuracies) * 100:.2f}, " + f"max: {numpy.max(final_test_accuracies) * 100:.2f}, " + f"5%: {numpy.percentile(final_test_accuracies, 5) * 100:.2f}, " + f"95%: {numpy.percentile(final_test_accuracies, 95) * 100:.2f}" + ) + # numpy.set_printoptions(threshold=sys.maxsize) + # print(f"trained soft weights: {repr(trained_state.params)}") + # hard_weights = harden.hard_weights(trained_state.params) + # print(f"trained hard weights: {repr(hard_weights)}") + + # Check symbolic net + _, hard, symbolic = neural_logic_net.net( + lambda type, x, training: nln(type, x, training) + ) + check_symbolic( + (soft, hard, symbolic), + (x_training, y_training, x_test, y_test), + trained_state, + dropout_rng, + ) diff --git a/tests/test_real_encoder.py b/tests/test_real_encoder.py index d653547..3fe61cb 100644 --- a/tests/test_real_encoder.py +++ b/tests/test_real_encoder.py @@ -3,18 +3,19 @@ import jax import numpy import optax +import pytest from flax.training import train_state from jax import random from jax.config import config -from neurallogic import (harden, neural_logic_net, real_encoder, - symbolic_generation) +from neurallogic import harden, neural_logic_net, real_encoder, symbolic_generation from tests import utils # Uncomment to debug NaNs # config.update("jax_debug_nans", True) +@pytest.mark.skip(reason="todo: upgrade to new version of jax") def check_consistency(soft: Callable, hard: Callable, expected, *args): # print(f'\nchecking consistency for {soft.__name__}') # Check that the soft function performs as expected @@ -36,6 +37,7 @@ def check_consistency(soft: Callable, hard: Callable, expected, *args): assert numpy.allclose(symbolic_output, hard_expected, equal_nan=True) +@pytest.mark.skip(reason="todo: upgrade to new version of jax") def test_activation(): test_data = [ [[1.0, 1.0], 0.5], @@ -57,6 +59,7 @@ def test_activation(): ) +@pytest.mark.skip(reason="todo: upgrade to new version of jax") def test_neuron(): test_data = [ [1.0, [1.0, 1.0, 0.6], [0.5, 0.5, 0.99999994]], @@ -77,11 +80,11 @@ def hard(thresholds, input): return real_encoder.hard_real_encoder_neuron(thresholds, input) check_consistency( - soft, hard, expected, jax.numpy.array( - thresholds), jax.numpy.array(input) + soft, hard, expected, jax.numpy.array(thresholds), jax.numpy.array(input) ) +@pytest.mark.skip(reason="todo: upgrade to new version of jax") def test_layer(): test_data = [ [ @@ -122,6 +125,7 @@ def hard(thresholds, input): ) +@pytest.mark.skip(reason="todo: upgrade to new version of jax") def test_real_encoder(): def test_net(type, x): return real_encoder.real_encoder_layer(type)(3)(x) @@ -173,6 +177,7 @@ def test_net(type, x): assert numpy.allclose(symbolic_output, hard_expected) +@pytest.mark.skip(reason="todo: upgrade to new version of jax") def test_train_real_encoder(): def test_net(type, x): return real_encoder.real_encoder_layer(type)(3)(x) @@ -202,8 +207,7 @@ def test_net(type, x): ) grad_fn = jax.jit( jax.value_and_grad( - lambda params, x, y: jax.numpy.mean( - (state.apply_fn(params, x) - y) ** 2) + lambda params, x, y: jax.numpy.mean((state.apply_fn(params, x) - y) ** 2) ) ) for epoch in range(1, 100): @@ -222,6 +226,7 @@ def test_net(type, x): assert jax.numpy.array_equal(symbolic_output, hard_expected) +@pytest.mark.skip(reason="todo: upgrade to new version of jax") def test_symbolic_real_encoder(): def test_net(type, x): return real_encoder.real_encoder_layer(type)(3)(x) @@ -229,7 +234,7 @@ def test_net(type, x): soft, hard, symbolic = neural_logic_net.net(test_net) # Compute soft result - soft_input = jax.numpy.array([1.0, 0.0]) + soft_input = jax.numpy.array([1, 0]) weights = soft.init(random.PRNGKey(0), soft_input) soft_result = soft.apply(weights, numpy.array(soft_input)) @@ -245,29 +250,29 @@ def test_net(type, x): assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and symbolic weights, but where the symbols can be evaluated - symbolic_input = ['1.0', '0.0'] + symbolic_input = ["1", "0"] symbolic_weights = utils.make_symbolic(hard_weights) symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) - symbolic_output = symbolic_generation.eval_symbolic_expression( - symbolic_output) + symbolic_output = symbolic_generation.eval_symbolic_expression(symbolic_output) # Check that the symbolic result is the same as the hard result assert numpy.array_equal(symbolic_output, hard_result) # Compute symbolic result with symbolic inputs and non-symbolic weights - symbolic_input = ['x1', 'x2'] + symbolic_input = ["x1", "x2"] symbolic_output = symbolic.apply(hard_weights, symbolic_input) + # Check the shape of the symbolic output + # TODO: activate this test when select_n is fully supported + # assert symbolic_output.shape == (2, 3) # Check the form of the symbolic expression - assert numpy.array_equal( - symbolic_output, - r'lax_reference.select(numpy.array(lax_reference.gt(lax_reference.select(numpy.numpy.array([[numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(0.07225775718688965, x1)), numpy.add(9.99999993922529e-09, numpy.multiply(9.999999747378752e-06, numpy.absolute(x1)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(numpy.absolute(x1), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(numpy.absolute(x1), inf)), lax_reference.eq(0.07225775718688965, x1))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x1, x1)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(0.06643760204315186, x1)), numpy.add(9.99999993922529e-09, numpy.multiply(9.999999747378752e-06, numpy.absolute(x1)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(numpy.absolute(x1), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(numpy.absolute(x1), inf)), lax_reference.eq(0.06643760204315186, x1))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x1, x1)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(0.9510347843170166, x1)), numpy.add(9.99999993922529e-09, numpy.multiply(9.999999747378752e-06, numpy.absolute(x1)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(numpy.absolute(x1), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(numpy.absolute(x1), inf)), lax_reference.eq(0.9510347843170166, x1))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x1, x1))))], [numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(0.8350926637649536, x2)), numpy.add(9.99999993922529e-09, numpy.multiply(9.999999747378752e-06, numpy.absolute(x2)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(numpy.absolute(x2), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(numpy.absolute(x2), inf)), lax_reference.eq(0.8350926637649536, x2))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x2, x2)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(0.8651731014251709, x2)), numpy.add(9.99999993922529e-09, numpy.multiply(9.999999747378752e-06, numpy.absolute(x2)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(numpy.absolute(x2), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(numpy.absolute(x2), inf)), lax_reference.eq(0.8651731014251709, x2))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x2, x2)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(0.6748189926147461, x2)), numpy.add(9.99999993922529e-09, numpy.multiply(9.999999747378752e-06, numpy.absolute(x2)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(numpy.absolute(x2), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(numpy.absolute(x2), inf)), lax_reference.eq(0.6748189926147461, x2))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x2, x2))))]], dtype=object), numpy.numpy.array([[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]], dtype=numpy.numpy.float32), lax_reference.select(numpy.numpy.array([[lax_reference.lt(x1, 0.07225775718688965), lax_reference.lt(x1, 0.06643760204315186), lax_reference.lt(x1, 0.9510347843170166)], [lax_reference.lt(x2, 0.8350926637649536), lax_reference.lt(x2, 0.8651731014251709), lax_reference.lt(x2, 0.6748189926147461)]], dtype=object), numpy.numpy.array([[numpy.multiply(6.9196672439575195, x1), numpy.multiply(7.525852680206299, x1), numpy.multiply(0.5257430672645569, x1)], [numpy.multiply(0.5987359285354614, x2), numpy.multiply(0.5779190063476562, x2), numpy.multiply(0.7409393787384033, x2)]], dtype=object), numpy.numpy.array([[numpy.multiply(0.5389427542686462, numpy.subtract(numpy.add(x1, 1.0), 0.1445155143737793)), numpy.multiply(0.5355827808380127, numpy.subtract(numpy.add(x1, 1.0), 0.1328752040863037)), numpy.multiply(10.211319923400879, numpy.subtract(numpy.add(x1, 1.0), 1.9020695686340332))], [numpy.multiply(3.0320050716400146, numpy.subtract(numpy.add(x2, 1.0), 1.6701853275299072)), numpy.multiply(3.7084574699401855, numpy.subtract(numpy.add(x2, 1.0), 1.7303462028503418)), numpy.multiply(1.5376049280166626, numpy.subtract(numpy.add(x2, 1.0), 1.3496379852294922))]], dtype=object))), 0.5), dtype=object), numpy.array([[ True, True, True], [ True, True, True]]), numpy.array([[False, False, False], [False, False, False]]))' - ) + expected_output = r"lax_reference.select(numpy.array(lax_reference.gt(lax_reference.select(numpy.numpy.array([[numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(lax_reference.abs(lax_reference.sub(0.07225775718688965, x1)), lax_reference.add(9.99999993922529e-09, lax_reference.mul(9.999999747378752e-06, lax_reference.abs(x1)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(lax_reference.abs(x1), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(lax_reference.abs(x1), inf)), lax_reference.eq(0.07225775718688965, x1))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x1, x1)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(lax_reference.abs(lax_reference.sub(0.06643760204315186, x1)), lax_reference.add(9.99999993922529e-09, lax_reference.mul(9.999999747378752e-06, lax_reference.abs(x1)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(lax_reference.abs(x1), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(lax_reference.abs(x1), inf)), lax_reference.eq(0.06643760204315186, x1))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x1, x1)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(lax_reference.abs(lax_reference.sub(0.9510347843170166, x1)), lax_reference.add(9.99999993922529e-09, lax_reference.mul(9.999999747378752e-06, lax_reference.abs(x1)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(lax_reference.abs(x1), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(lax_reference.abs(x1), inf)), lax_reference.eq(0.9510347843170166, x1))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x1, x1))))], [numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(lax_reference.abs(lax_reference.sub(0.8350926637649536, x2)), lax_reference.add(9.99999993922529e-09, lax_reference.mul(9.999999747378752e-06, lax_reference.abs(x2)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(lax_reference.abs(x2), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(lax_reference.abs(x2), inf)), lax_reference.eq(0.8350926637649536, x2))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x2, x2)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(lax_reference.abs(lax_reference.sub(0.8651731014251709, x2)), lax_reference.add(9.99999993922529e-09, lax_reference.mul(9.999999747378752e-06, lax_reference.abs(x2)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(lax_reference.abs(x2), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(lax_reference.abs(x2), inf)), lax_reference.eq(0.8651731014251709, x2))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x2, x2)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(lax_reference.abs(lax_reference.sub(0.6748189926147461, x2)), lax_reference.add(9.99999993922529e-09, lax_reference.mul(9.999999747378752e-06, lax_reference.abs(x2)))), numpy.logical_not(numpy.logical_or(False, lax_reference.eq(lax_reference.abs(x2), inf)))), numpy.logical_and(numpy.logical_and(False, lax_reference.eq(lax_reference.abs(x2), inf)), lax_reference.eq(0.6748189926147461, x2))), numpy.logical_not(numpy.logical_or(False, lax_reference.ne(x2, x2))))]], dtype=object), numpy.numpy.array([[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]], dtype=numpy.numpy.float32), lax_reference.select(numpy.numpy.array([[lax_reference.lt(x1, 0.07225775718688965), lax_reference.lt(x1, 0.06643760204315186), lax_reference.lt(x1, 0.9510347843170166)], [lax_reference.lt(x2, 0.8350926637649536), lax_reference.lt(x2, 0.8651731014251709), lax_reference.lt(x2, 0.6748189926147461)]], dtype=object), numpy.numpy.array([[lax_reference.div(x1, 0.14451561868190765), lax_reference.div(x1, 0.13287530839443207), lax_reference.div(x1, 1.9020696878433228)], [lax_reference.div(x2, 1.6701854467391968), lax_reference.div(x2, 1.7303463220596313), lax_reference.div(x2, 1.3496381044387817)]], dtype=object), numpy.numpy.array([[lax_reference.div(lax_reference.sub(lax_reference.add(x1, 1), 0.1445155143737793), 1.8554846048355103), lax_reference.div(lax_reference.sub(lax_reference.add(x1, 1), 0.1328752040863037), 1.8671249151229858), lax_reference.div(lax_reference.sub(lax_reference.add(x1, 1), 1.9020695686340332), 0.09793052822351456)], [lax_reference.div(lax_reference.sub(lax_reference.add(x2, 1), 1.6701853275299072), 0.32981476187705994), lax_reference.div(lax_reference.sub(lax_reference.add(x2, 1), 1.7303462028503418), 0.26965388655662537), lax_reference.div(lax_reference.sub(lax_reference.add(x2, 1), 1.3496379852294922), 0.6503621339797974)]], dtype=object))), 0.5), dtype=object), numpy.array([[ True, True, True], [ True, True, True]]), numpy.array([[False, False, False], [False, False, False]]))" + assert numpy.array_equal(symbolic_output, expected_output) # Compute symbolic result with symbolic inputs and symbolic weights symbolic_output = symbolic.apply(symbolic_weights, symbolic_input) + # Check the shape of the symbolic expression + # TODO: activate this test when select_n is fully supported + # assert symbolic_output.shape == (2, 3) # Check the form of the symbolic expression # N.B. expected output can change depending due to presence of small numerical errors that can differ between runs and platforms - expected_output = r'lax_reference.select(lax_reference.gt(lax_reference.select(numpy.array([[numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776)), x1)), numpy.add(1e-08, numpy.multiply(1e-05, numpy.absolute(x1)))), numpy.logical_not(numpy.logical_or(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776))), inf), lax_reference.eq(numpy.absolute(x1), inf)))), numpy.logical_and(numpy.logical_and(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776))), inf), lax_reference.eq(numpy.absolute(x1), inf)), lax_reference.eq(numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776)), x1))), numpy.logical_not(numpy.logical_or(lax_reference.ne(numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776)), numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776))), lax_reference.ne(x1, x1)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376)), x1)), numpy.add(1e-08, numpy.multiply(1e-05, numpy.absolute(x1)))), numpy.logical_not(numpy.logical_or(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376))), inf), lax_reference.eq(numpy.absolute(x1), inf)))), numpy.logical_and(numpy.logical_and(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376))), inf), lax_reference.eq(numpy.absolute(x1), inf)), lax_reference.eq(numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376)), x1))), numpy.logical_not(numpy.logical_or(lax_reference.ne(numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376)), numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376))), lax_reference.ne(x1, x1)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348)), x1)), numpy.add(1e-08, numpy.multiply(1e-05, numpy.absolute(x1)))), numpy.logical_not(numpy.logical_or(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348))), inf), lax_reference.eq(numpy.absolute(x1), inf)))), numpy.logical_and(numpy.logical_and(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348))), inf), lax_reference.eq(numpy.absolute(x1), inf)), lax_reference.eq(numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348)), x1))), numpy.logical_not(numpy.logical_or(lax_reference.ne(numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348)), numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348))), lax_reference.ne(x1, x1))))], [numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266)), x2)), numpy.add(1e-08, numpy.multiply(1e-05, numpy.absolute(x2)))), numpy.logical_not(numpy.logical_or(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266))), inf), lax_reference.eq(numpy.absolute(x2), inf)))), numpy.logical_and(numpy.logical_and(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266))), inf), lax_reference.eq(numpy.absolute(x2), inf)), lax_reference.eq(numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266)), x2))), numpy.logical_not(numpy.logical_or(lax_reference.ne(numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266)), numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266))), lax_reference.ne(x2, x2)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731)), x2)), numpy.add(1e-08, numpy.multiply(1e-05, numpy.absolute(x2)))), numpy.logical_not(numpy.logical_or(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731))), inf), lax_reference.eq(numpy.absolute(x2), inf)))), numpy.logical_and(numpy.logical_and(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731))), inf), lax_reference.eq(numpy.absolute(x2), inf)), lax_reference.eq(numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731)), x2))), numpy.logical_not(numpy.logical_or(lax_reference.ne(numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731)), numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731))), lax_reference.ne(x2, x2)))), numpy.logical_and(numpy.logical_or(numpy.logical_and(lax_reference.le(numpy.absolute(numpy.subtract(numpy.minimum(1.0, numpy.maximum(0.0, 0.674819)), x2)), numpy.add(1e-08, numpy.multiply(1e-05, numpy.absolute(x2)))), numpy.logical_not(numpy.logical_or(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.674819))), inf), lax_reference.eq(numpy.absolute(x2), inf)))), numpy.logical_and(numpy.logical_and(lax_reference.eq(numpy.absolute(numpy.minimum(1.0, numpy.maximum(0.0, 0.674819))), inf), lax_reference.eq(numpy.absolute(x2), inf)), lax_reference.eq(numpy.minimum(1.0, numpy.maximum(0.0, 0.674819)), x2))), numpy.logical_not(numpy.logical_or(lax_reference.ne(numpy.minimum(1.0, numpy.maximum(0.0, 0.674819)), numpy.minimum(1.0, numpy.maximum(0.0, 0.674819))), lax_reference.ne(x2, x2))))]], dtype=object), numpy.array([[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]), lax_reference.select(numpy.array([[lax_reference.lt(x1, numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776))), lax_reference.lt(x1, numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376))), lax_reference.lt(x1, numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348)))], [lax_reference.lt(x2, numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266))), lax_reference.lt(x2, numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731))), lax_reference.lt(x2, numpy.minimum(1.0, numpy.maximum(0.0, 0.674819)))]], dtype=object), numpy.array([[numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776))), 1e-07)), x1), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376))), 1e-07)), x1), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348))), 1e-07)), x1)], [numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266))), 1e-07)), x2), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731))), 1e-07)), x2), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.674819))), 1e-07)), x2)]], dtype=object), numpy.array([[numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.subtract(1.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776)))), 1e-07)), numpy.subtract(numpy.add(x1, 1.0), numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.07225776))))), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.subtract(1.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376)))), 1e-07)), numpy.subtract(numpy.add(x1, 1.0), numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.0664376))))), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.subtract(1.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348)))), 1e-07)), numpy.subtract(numpy.add(x1, 1.0), numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.9510348)))))], [numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.subtract(1.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266)))), 1e-07)), numpy.subtract(numpy.add(x2, 1.0), numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.83509266))))), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.subtract(1.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731)))), 1e-07)), numpy.subtract(numpy.add(x2, 1.0), numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.8651731))))), numpy.multiply(lax_reference.div(1.0, numpy.add(numpy.multiply(2.0, numpy.subtract(1.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.674819)))), 1e-07)), numpy.subtract(numpy.add(x2, 1.0), numpy.multiply(2.0, numpy.minimum(1.0, numpy.maximum(0.0, 0.674819)))))]], dtype=object))), 0.5), numpy.array([[ True, True, True], [ True, True, True]]), numpy.array([[False, False, False], [False, False, False]]))' - assert numpy.array_equal( - symbolic_output, - expected_output - ) + expected_output = r"lax_reference.select(lax_reference.gt(lax_reference.select(numpy.array([[lax_reference.eq(lax_reference.min(1, lax_reference.max(0, 0.07225776)), x1), lax_reference.eq(lax_reference.min(1, lax_reference.max(0, 0.0664376)), x1), lax_reference.eq(lax_reference.min(1, lax_reference.max(0, 0.9510348)), x1)], [lax_reference.eq(lax_reference.min(1, lax_reference.max(0, 0.83509266)), x2), lax_reference.eq(lax_reference.min(1, lax_reference.max(0, 0.8651731)), x2), lax_reference.eq(lax_reference.min(1, lax_reference.max(0, 0.674819)), x2)]], dtype=object), numpy.array([[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]), lax_reference.select(numpy.array([[lax_reference.lt(x1, lax_reference.min(1, lax_reference.max(0, 0.07225776))), lax_reference.lt(x1, lax_reference.min(1, lax_reference.max(0, 0.0664376))), lax_reference.lt(x1, lax_reference.min(1, lax_reference.max(0, 0.9510348)))], [lax_reference.lt(x2, lax_reference.min(1, lax_reference.max(0, 0.83509266))), lax_reference.lt(x2, lax_reference.min(1, lax_reference.max(0, 0.8651731))), lax_reference.lt(x2, lax_reference.min(1, lax_reference.max(0, 0.674819)))]], dtype=object), numpy.array([[lax_reference.div(x1, lax_reference.add(lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.07225776))), 1e-07)), lax_reference.div(x1, lax_reference.add(lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.0664376))), 1e-07)), lax_reference.div(x1, lax_reference.add(lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.9510348))), 1e-07))], [lax_reference.div(x2, lax_reference.add(lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.83509266))), 1e-07)), lax_reference.div(x2, lax_reference.add(lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.8651731))), 1e-07)), lax_reference.div(x2, lax_reference.add(lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.674819))), 1e-07))]], dtype=object), numpy.array([[lax_reference.div(lax_reference.sub(lax_reference.add(x1, 1), lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.07225776)))), lax_reference.add(lax_reference.mul(2, lax_reference.sub(1, lax_reference.min(1, lax_reference.max(0, 0.07225776)))), 1e-07)), lax_reference.div(lax_reference.sub(lax_reference.add(x1, 1), lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.0664376)))), lax_reference.add(lax_reference.mul(2, lax_reference.sub(1, lax_reference.min(1, lax_reference.max(0, 0.0664376)))), 1e-07)), lax_reference.div(lax_reference.sub(lax_reference.add(x1, 1), lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.9510348)))), lax_reference.add(lax_reference.mul(2, lax_reference.sub(1, lax_reference.min(1, lax_reference.max(0, 0.9510348)))), 1e-07))], [lax_reference.div(lax_reference.sub(lax_reference.add(x2, 1), lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.83509266)))), lax_reference.add(lax_reference.mul(2, lax_reference.sub(1, lax_reference.min(1, lax_reference.max(0, 0.83509266)))), 1e-07)), lax_reference.div(lax_reference.sub(lax_reference.add(x2, 1), lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.8651731)))), lax_reference.add(lax_reference.mul(2, lax_reference.sub(1, lax_reference.min(1, lax_reference.max(0, 0.8651731)))), 1e-07)), lax_reference.div(lax_reference.sub(lax_reference.add(x2, 1), lax_reference.mul(2, lax_reference.min(1, lax_reference.max(0, 0.674819)))), lax_reference.add(lax_reference.mul(2, lax_reference.sub(1, lax_reference.min(1, lax_reference.max(0, 0.674819)))), 1e-07))]], dtype=object))), 0.5), numpy.array([[ True, True, True], [ True, True, True]]), numpy.array([[False, False, False], [False, False, False]]))" + assert numpy.array_equal(symbolic_output, expected_output) diff --git a/tests/test_symbolic_generation.py b/tests/test_symbolic_generation.py index 0972b2e..e715455 100644 --- a/tests/test_symbolic_generation.py +++ b/tests/test_symbolic_generation.py @@ -1,32 +1,33 @@ +import flax import jax import jax.numpy as jnp import numpy -from neurallogic import (hard_not, hard_or, harden, harden_layer, - neural_logic_net, symbolic_generation, - symbolic_primitives) -from tests import test_mnist, utils +from neurallogic import (hard_and, hard_majority, hard_not, hard_or, hard_xor, + harden, harden_layer, neural_logic_net, real_encoder, + symbolic_generation, hard_concatenate, hard_vmap, symbolic_primitives) +from tests import utils def nln(type, x, width): + # Can't symbolically support this layer yet since the symbolic output is an unevaluated string that + # lacks the correct tensor structure + # x = real_encoder.real_encoder_layer(type)(2)(x) + # x = x.ravel() + y = hard_vmap.vmap(type)((lambda x: 1 - x, lambda x: 1 - x, lambda x: symbolic_primitives.symbolic_not(x)))(x) + x = hard_concatenate.concatenate(type)([x, y], 0) x = hard_or.or_layer(type)(width)(x) - x = hard_not.not_layer(type)(10)(x) - x = x.ravel() + x = hard_and.and_layer(type)(width)(x) + x = hard_xor.xor_layer(type)(width)(x) + x = hard_not.not_layer(type)(2)(x) + x = hard_majority.majority_layer(type)()(x) x = harden_layer.harden_layer(type)(x) - x = x.reshape((10, width)) + x = x.reshape([2, 1]) x = x.sum(-1) return x def test_symbolic_generation(): - # Get MNIST dataset - train_ds, test_ds = test_mnist.get_datasets() - # Flatten images - train_ds["image"] = jnp.reshape( - train_ds["image"], (train_ds["image"].shape[0], -1)) - test_ds["image"] = jnp.reshape( - test_ds["image"], (test_ds["image"].shape[0], -1)) - # Define width of network width = 2 # Define the neural logic net @@ -34,27 +35,25 @@ def test_symbolic_generation(): lambda type, x: nln(type, x, width)) # Initialize a random number generator rng = jax.random.PRNGKey(0) - rng, init_rng = jax.random.split(rng) - mock_input = harden.harden(jnp.ones([28 * 28])) + #rng, init_rng = jax.random.split(rng) + mock_input = harden.harden(jnp.ones([2 * 2])) # Initialize the weights of the neural logic net - hard_weights = harden.hard_weights(soft.init(rng, mock_input)) - # Define a hard mock input - hard_mock_input = harden.harden(test_ds['image'][0]) + soft_weights = soft.init(rng, mock_input) + hard_weights = harden.hard_weights(soft_weights) # Apply the neural logic net to the hard input - hard_output = hard.apply(hard_weights, hard_mock_input) + hard_output = hard.apply(hard_weights, mock_input) # Check the standard evaluation of the network equals the non-standard evaluation - symbolic_output = symbolic.apply(hard_weights, hard_mock_input) + symbolic_weights = harden.hard_weights(soft_weights) + symbolic_output = symbolic.apply(symbolic_weights, mock_input) assert numpy.array_equal(symbolic_output, hard_output) # Check the standard evaluation of the network equals the non-standard symbolic evaluation - symbolic_mock_input = utils.make_symbolic(hard_mock_input) - symbolic_output = symbolic.apply(hard_weights, symbolic_mock_input) + symbolic_mock_input = utils.make_symbolic(mock_input) + symbolic_output = symbolic.apply(symbolic_weights, symbolic_mock_input) assert numpy.array_equal(hard_output.shape, symbolic_output.shape) # Compute the symbolic expression, i.e. perform the actual operations in the symbolic expression - #print(f'symbolic_output: {symbolic_output}') - # TODO: We cannot evaluate the symbolic expression because it has too many nested parantheses - #eval_symbolic_output = symbolic_generation.eval_symbolic_expression(symbolic_output) + eval_symbolic_output = symbolic_generation.eval_symbolic_expression(symbolic_output) # If this assertion succeeds then the non-standard symbolic evaluation of the jaxpr is is identical to the standard evaluation of network - #assert numpy.array_equal(hard_output, eval_symbolic_output) + assert numpy.array_equal(hard_output, eval_symbolic_output) diff --git a/tests/test_toy_problem.py b/tests/test_toy_problem.py new file mode 100644 index 0000000..935dd52 --- /dev/null +++ b/tests/test_toy_problem.py @@ -0,0 +1,359 @@ +from pathlib import Path + +import jax +import ml_collections +import numpy +import pytest +import optax +import scipy +from flax.training import train_state +from jax.config import config +from tqdm import tqdm + +from neurallogic import ( + hard_and, + hard_dropout, + hard_majority, + hard_masks, + hard_not, + hard_or, + hard_xor, + hard_count, + harden, + harden_layer, + neural_logic_net, + real_encoder, + initialization, + hard_vmap, + hard_concatenate, + symbolic_primitives +) +from tests import utils + +config.update("jax_enable_x64", True) + +""" +Temperature: 4 booleans, 1-hot vector + 0 high = very cold + 1 high = cold + 2 high = warm + 3 high = very warm +Outside?: 1 boolean + 0 = no + 1 = yes +Labels: + 0 = wear t-shirt + 1 = wear coat +""" + +toy_data = 2 +num_classes = 2 +if toy_data == 1: + num_features = 1 +else: + num_features = 5 + + +def check_symbolic(nets, data, trained_state, dropout_rng): + x_training, y_training, x_test, y_test = data + _, hard, symbolic = nets + _, test_loss, test_accuracy = apply_model_with_grad(trained_state, x_test, y_test, dropout_rng) + print( + "soft_net: final test_loss: %.4f, final test_accuracy: %.2f" + % (test_loss, test_accuracy * 100) + ) + hard_weights = harden.hard_weights(trained_state.params) + hard_trained_state = TrainState.create( + apply_fn=hard.apply, + params=hard_weights, + tx=optax.sgd(1.0, 1.0), + dropout_rng=dropout_rng, + ) + hard_input = harden.harden(x_test) + hard_test_accuracy = apply_hard_model_to_data(hard_trained_state, hard_input, y_test) + print("hard_net: final test_accuracy: %.2f" % (hard_test_accuracy * 100)) + assert numpy.isclose(test_accuracy, hard_test_accuracy, atol=0.0001) + + # CPU and GPU give different results, so we can't easily regress on a static symbolic expression + if toy_data == 1: + symbolic_input = ["outside"] + else: + symbolic_input = ["very-cold", "cold", "warm", "very-warm", "outside"] + # This simply checks that the symbolic output can be generated + symbolic_output = symbolic.apply({"params": hard_weights}, symbolic_input, training=False) + print("symbolic_output: class 1", symbolic_output[0][:10000]) + print("symbolic_output: class 2", symbolic_output[1][:10000]) + + +def nln_1(type, x, training: bool): + dtype = jax.numpy.float32 + layer_size = 2 + x = hard_not.not_layer(type)(layer_size)(x) + x = x.ravel() + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = hard_majority.majority_layer(type)()(x) + ######################################################## + x = harden_layer.harden_layer(type)(x) + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = x.sum(-1) + return x + +""" +Class 1: +lax_reference.ge(lax_reference.sum((0, numpy.logical_not(numpy.logical_xor(lax_reference.ne(x0, 0), False)))), 1) + +is equivalent to: + +sum( + ( + 0, + ! xor(x0 != 0, False) + ) +) >= 1 + +is equivalent to: + +! xor(x0 != 0, False) >= 1 + +is equivalent to: + +! x0 + +Class 2: +class 2 lax_reference.ge(lax_reference.sum((0, numpy.logical_not(numpy.logical_xor(lax_reference.ne(x0, 0), True)))), 1) + +is equivalent to: + +! xor(x0 != 0, True) >= 1 + +is equivalent to: + +x0 + +Therefore learned class prediction is [!x, x] +""" + +def nln_2(type, x, training: bool): + dtype = jax.numpy.float32 + x = hard_not.not_layer(type)(8)(x) + x = x.ravel() + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = hard_majority.majority_layer(type)()(x) + ######################################################## + x = harden_layer.harden_layer(type)(x) + x = x.reshape((num_classes, int(x.shape[0] / num_classes))) + x = x.sum(-1) + return x + +def nln(type, x, training: bool): + if toy_data == 1: + return nln_1(type, x, training) + else: + return nln_2(type, x, training) + +def batch_nln(type, x, training: bool): + return jax.vmap(lambda x: nln(type, x, training))(x) + + +class TrainState(train_state.TrainState): + dropout_rng: jax.random.KeyArray + + +def create_train_state(net, rng, dropout_rng, config): + mock_input = jax.numpy.ones([1, num_features]) + soft_weights = net.init(rng, mock_input, training=False)["params"] + tx = optax.radam(learning_rate=config.learning_rate) + return TrainState.create( + apply_fn=net.apply, params=soft_weights, tx=tx, dropout_rng=dropout_rng + ) + + +@jax.jit +def update_model(state, grads): + return state.apply_gradients(grads=grads) + +def apply_model_with_grad_impl(state, features, labels, dropout_rng, training: bool): + dropout_train_rng = jax.random.fold_in(key=dropout_rng, data=state.step) + + def loss_fn(params): + logits = state.apply_fn( + {"params": params}, + features, + training=training, + rngs={"dropout": dropout_train_rng}, + ) + one_hot = jax.nn.one_hot(labels, num_classes) + loss = jax.numpy.mean( + optax.softmax_cross_entropy(logits=logits, labels=one_hot) + ) + return loss, logits + + grad_fn = jax.value_and_grad(loss_fn, has_aux=True) + (loss, logits), grads = grad_fn(state.params) + accuracy = jax.numpy.mean(jax.numpy.argmax(logits, -1) == labels) + return grads, loss, accuracy + + +@jax.jit +def apply_model_with_grad_and_training(state, features, labels, dropout_rng): + return apply_model_with_grad_impl( + state, features, labels, dropout_rng, training=True + ) + + +@jax.jit +def apply_model_with_grad(state, features, labels, dropout_rng): + return apply_model_with_grad_impl( + state, features, labels, dropout_rng, training=False + ) + + +def train_epoch(state, features, labels, batch_size, rng, dropout_rng): + train_ds_size = len(features) + steps_per_epoch = train_ds_size // batch_size + + perms = jax.random.permutation(rng, len(features)) + perms = perms[: steps_per_epoch * batch_size] # skip incomplete batch + perms = perms.reshape((steps_per_epoch, batch_size)) + + epoch_loss = [] + epoch_accuracy = [] + + for perm in perms: + batch_features = features[perm, ...] + batch_labels = labels[perm, ...] + grads, loss, accuracy = apply_model_with_grad_and_training( + state, batch_features, batch_labels, dropout_rng + ) + state = update_model(state, grads) + epoch_loss.append(loss) + epoch_accuracy.append(accuracy) + train_loss = numpy.mean(epoch_loss) + train_accuracy = numpy.mean(epoch_accuracy) + return state, train_loss, train_accuracy + + +def train_and_evaluate( + init_rng, dropout_rng, net, data, config: ml_collections.ConfigDict +): + state = create_train_state(net, init_rng, dropout_rng, config) + x_training, y_training, x_test, y_test = data + best_train_accuracy = 0.0 + best_test_accuracy = 0.0 + for epoch in range(1, config.num_epochs + 1): + init_rng, input_rng = jax.random.split(init_rng) + state, train_loss, train_accuracy = train_epoch( + state, x_training, y_training, config.batch_size, input_rng, dropout_rng + ) + _, test_loss, test_accuracy = apply_model_with_grad( + state, x_test, y_test, dropout_rng + ) + if train_accuracy > best_train_accuracy: + best_train_accuracy = train_accuracy + if test_accuracy >= best_test_accuracy: + best_test_accuracy = test_accuracy + print( + "epoch:% 3d, train_loss: %.4f, train_accuracy: %.2f, test_loss: %.4f, test_accuracy: %.2f" + % (epoch, train_loss, train_accuracy * 100, test_loss, test_accuracy * 100) + ) + if train_accuracy == 1.0 and test_accuracy == 1.0: + break + + # return trained state and final test_accuracy + return state, test_accuracy + + +def apply_hard_model(state, features, label): + def logits_fn(params): + return state.apply_fn({"params": params}, features, training=False) + + logits = logits_fn(state.params) + if isinstance(logits, list): + logits = jax.numpy.array(logits) + logits *= 1.0 + accuracy = jax.numpy.mean(jax.numpy.argmax(logits, -1) == label) + return accuracy + + +def apply_hard_model_to_data(state, features, labels): + accuracy = 0 + for image, label in tqdm(zip(features, labels), total=len(features)): + accuracy += apply_hard_model(state, image, label) + return accuracy / len(features) + + +def get_config(): + config = ml_collections.ConfigDict() + config.learning_rate = 0.01 + config.momentum = 0.9 + if toy_data == 1: + config.batch_size = 16 + else: + config.batch_size = 48 + config.num_epochs = 1000 + return config + +def get_toy_data(): + data_dir = Path(__file__).parent.parent / "tests" / "data" + if toy_data == 1: + data = numpy.loadtxt(data_dir / "toy_data_1.txt").astype(dtype=numpy.int32) + else: + data = numpy.loadtxt(data_dir / "toy_data_2.txt").astype(dtype=numpy.int32) + features = data[:, 0:num_features] # Input features + labels = data[:, num_features] # Target value + return features, labels + + +def train_test_split(features, labels, rng, test_size=0.2): + rng, split_rng = jax.random.split(rng) + train_size = int(len(features) * (1 - test_size)) + train_idx = jax.random.permutation(split_rng, len(features))[:train_size] + test_idx = jax.random.permutation(split_rng, len(features))[train_size:] + return ( + features[train_idx], + features[test_idx], + labels[train_idx], + labels[test_idx], + ) + +@pytest.mark.skip(reason="temporarily off") +def test_toy(): + # Train net + features, labels = get_toy_data() + soft, hard, symbolic = neural_logic_net.net( + lambda type, x, training: batch_nln(type, x, training) + ) + + rng = jax.random.PRNGKey(0) + print(soft.tabulate(rng, features[0:1], training=False)) + + num_experiments = 1 + final_test_accuracies = [] + for i in range(num_experiments): + # Split features and labels into 80% training and 20% test + rng, int_rng, dropout_rng = jax.random.split(rng, 3) + x_training, x_test, y_training, y_test = train_test_split( + features, labels, rng, test_size=0.2 + ) + trained_state, final_test_accuracy = train_and_evaluate( + int_rng, + dropout_rng, + soft, + (x_training, y_training, x_test, y_test), + get_config(), + ) + final_test_accuracies.append(final_test_accuracy) + print(f"{i}: final test accuracy: {final_test_accuracy * 100:.2f}") + # print mean, standard error of the mean, min, max, lowest 5%, highest 5% of final test accuracies + print( + f"mean: {numpy.mean(final_test_accuracies) * 100:.2f}, " + f"sem: {scipy.stats.sem(final_test_accuracies) * 100:.2f}, " + f"min: {numpy.min(final_test_accuracies) * 100:.2f}, " + f"max: {numpy.max(final_test_accuracies) * 100:.2f}, " + f"5%: {numpy.percentile(final_test_accuracies, 5) * 100:.2f}, " + f"95%: {numpy.percentile(final_test_accuracies, 95) * 100:.2f}" + ) + + # Check symbolic net + _, hard, symbolic = neural_logic_net.net(lambda type, x, training: nln(type, x, training)) + check_symbolic((soft, hard, symbolic), (x_training, y_training, x_test, y_test), trained_state, dropout_rng) diff --git a/tests/utils.py b/tests/utils.py index 58e01ec..21f9219 100644 --- a/tests/utils.py +++ b/tests/utils.py @@ -72,21 +72,21 @@ def make_symbolic(*args): def check_consistency(soft: Callable, hard: Callable, expected, *args): - #print(f'\nchecking consistency for {soft.__name__}') + print(f'\nchecking consistency for {soft.__name__}') # Check that the soft function performs as expected soft_output = soft(*args) - #print(f'Expected: {expected}, Actual soft_output: {soft_output}') + print(f'Expected: {expected}, Actual soft_output: {repr(soft_output)}') assert numpy.allclose(soft_output, expected, equal_nan=True) # Check that the hard function performs as expected - hard_args = harden.harden(*args) + hard_args = tuple([harden.harden(arg) for arg in args]) hard_expected = harden.harden(expected) hard_output = hard(*hard_args) - #print(f'Expected: {hard_expected}, Actual hard_output: {hard_output}') + print(f'Expected: {hard_expected}, Actual hard_output: {repr(hard_output)}') assert numpy.allclose(hard_output, hard_expected, equal_nan=True) # Check that the jaxpr performs as expected symbolic_f = symbolic_generation.make_symbolic_jaxpr(hard, *hard_args) symbolic_output = symbolic_generation.eval_symbolic(symbolic_f, *hard_args) - #print(f'Expected: {hard_expected}, Actual symbolic_output: {symbolic_output}') + print(f'Expected: {hard_expected}, Actual symbolic_output: {repr(symbolic_output)}') assert numpy.allclose(symbolic_output, hard_expected, equal_nan=True)