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2020 – today
- 2024
[j12]Clemens Karner, Vladimir A. Kazeev, Philipp Christian Petersen
:
Limitations of neural network training due to numerical instability of backpropagation. Adv. Comput. Math. 50(1): 14 (2024)- [j11]Philipp Christian Petersen, Anna Sepliarskaia:
VC dimensions of group convolutional neural networks. Neural Networks 169: 462-474 (2024) - [i26]A. Martina Neuman, Philipp Christian Petersen:
Efficient Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders. CoRR abs/2404.04549 (2024) - [i25]Adeyemi D. Adeoye, Philipp Christian Petersen, Alberto Bemporad:
Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks. CoRR abs/2404.14875 (2024) - [i24]Philipp Petersen, Jakob Zech:
Mathematical theory of deep learning. CoRR abs/2407.18384 (2024) - [i23]Andrés Felipe Lerma Pineda, Philipp Petersen, Simon Frieder, Thomas Lukasiewicz:
Dimension-independent learning rates for high-dimensional classification problems. CoRR abs/2409.17991 (2024) - [i22]Joost A. A. Opschoor, Philipp Christian Petersen, Christoph Schwab:
First Order System Least Squares Neural Networks. CoRR abs/2409.20264 (2024) - [i21]Yuanyuan Li, Philipp Grohs, Philipp Petersen:
The sampling complexity of learning invertible residual neural networks. CoRR abs/2411.05453 (2024) - [i20]Jonathan Garcia, Philipp Petersen:
High-dimensional classification problems with Barron regular boundaries under margin conditions. CoRR abs/2412.07312 (2024) - 2023
- [j10]Carlo Marcati, Joost A. A. Opschoor, Philipp Christian Petersen, Christoph Schwab:
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities. Found. Comput. Math. 23(3): 1043-1127 (2023) - [c1]Simon Frieder, Luca Pinchetti, Alexis Chevalier, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Petersen, Julius Berner:
Mathematical Capabilities of ChatGPT. NeurIPS 2023 - [i19]Simon Frieder, Luca Pinchetti, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Christian Petersen, Alexis Chevalier, Julius Berner:
Mathematical Capabilities of ChatGPT. CoRR abs/2301.13867 (2023) - [i18]Simon Frieder, Julius Berner, Philipp Petersen, Thomas Lukasiewicz:
Large Language Models for Mathematicians. CoRR abs/2312.04556 (2023) - 2022
- [i17]Andrés Felipe Lerma Pineda, Philipp Christian Petersen:
Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems. CoRR abs/2206.00934 (2022) - [i16]Clemens Karner, Vladimir A. Kazeev, Philipp Christian Petersen:
Limitations of neural network training due to numerical instability of backpropagation. CoRR abs/2210.00805 (2022) - [i15]Philipp Christian Petersen, Anna Sepliarskaia:
VC dimensions of group convolutional neural networks. CoRR abs/2212.09507 (2022) - 2021
- [j9]Fabian Laakmann, Philipp Petersen:
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs. Adv. Comput. Math. 47(1): 11 (2021) - [j8]Philipp Petersen, Mones Raslan, Felix Voigtländer:
Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size. Found. Comput. Math. 21(2): 375-444 (2021) - [j7]Moritz Geist, Philipp Petersen, Mones Raslan, Reinhold Schneider, Gitta Kutyniok:
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks. J. Sci. Comput. 88(1): 22 (2021) - [i14]Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen:
The Modern Mathematics of Deep Learning. CoRR abs/2105.04026 (2021) - [i13]Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen:
Deep Microlocal Reconstruction for Limited-Angle Tomography. CoRR abs/2108.05732 (2021) - [i12]Philipp Petersen, Felix Voigtländer:
Optimal learning of high-dimensional classification problems using deep neural networks. CoRR abs/2112.12555 (2021) - 2020
- [j6]Philipp Grohs, Gitta Kutyniok, Jackie Ma, Philipp Petersen, Mones Raslan:
Anisotropic multiscale systems on bounded domains. Adv. Comput. Math. 46(2): 39 (2020) - [i11]Fabian Laakmann, Philipp Petersen:
Efficient Approximation of Solutions of Parametric Linear Transport Equations by ReLU DNNs. CoRR abs/2001.11441 (2020) - [i10]Moritz Geist, Philipp Petersen, Mones Raslan, Reinhold Schneider, Gitta Kutyniok:
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks. CoRR abs/2004.12131 (2020) - [i9]Carlo Marcati, Joost A. A. Opschoor, Philipp Christian Petersen, Christoph Schwab:
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities. CoRR abs/2010.12217 (2020)
2010 – 2019
- 2019
- [j5]Philipp Petersen, Mones Raslan:
Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces. Adv. Comput. Math. 45(3): 1581-1606 (2019) - [j4]Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen:
Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks. SIAM J. Imaging Sci. 12(4): 1936-1966 (2019) - [j3]Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen:
Optimal Approximation with Sparsely Connected Deep Neural Networks. SIAM J. Math. Data Sci. 1(1): 8-45 (2019) - [i8]Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen:
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks. CoRR abs/1901.01388 (2019) - [i7]Dominik Alfke, Weston Baines, Jan Blechschmidt, Mauricio J. del Razo Sarmina, Amnon Drory, Dennis Elbrächter, Nando Farchmin, Matteo Gambara, Silke Glas, Philipp Grohs, Peter Hinz, Danijel Kivaranovic, Christian Kümmerle, Gitta Kutyniok, Sebastian Lunz, Jan MacDonald, Ryan Malthaner, Gregory Naisat, Ariel Neufeld, Philipp Christian Petersen, Rafael Reisenhofer, Jun-Da Sheng, Laura Thesing, Philipp Trunschke, Johannes von Lindheim, David Weber, Melanie Weber:
The Oracle of DLphi. CoRR abs/1901.05744 (2019) - [i6]Ingo Gühring, Gitta Kutyniok, Philipp Petersen:
Error bounds for approximations with deep ReLU neural networks in $W^{s, p}$ norms. CoRR abs/1902.07896 (2019) - [i5]Gitta Kutyniok, Philipp Petersen, Mones Raslan, Reinhold Schneider:
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs. CoRR abs/1904.00377 (2019) - [i4]Felix Voigtländer, Philipp Petersen:
Approximation in Lp(μ) with deep ReLU neural networks. CoRR abs/1904.04789 (2019) - 2018
- [j2]Philipp Petersen, Felix Voigtländer:
Optimal approximation of piecewise smooth functions using deep ReLU neural networks. Neural Networks 108: 296-330 (2018) - [i3]Philipp Petersen, Felix Voigtländer:
Equivalence of approximation by convolutional neural networks and fully-connected networks. CoRR abs/1809.00973 (2018) - 2017
- [i2]Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen:
Optimal Approximation with Sparsely Connected Deep Neural Networks. CoRR abs/1705.01714 (2017) - [i1]Philipp Petersen, Felix Voigtländer:
Optimal approximation of piecewise smooth functions using deep ReLU neural networks. CoRR abs/1709.05289 (2017) - 2016
- [j1]Philipp Petersen:
Shearlet approximation of functions with discontinuous derivatives. J. Approx. Theory 207: 127-138 (2016)
Coauthor Index
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