Algorithm 25: Sigma-Adaptive Logit Tail-Free Sampling (σ-L-TFS)
Required: Logits tensor L, scale S ∈ (0,1), decay_rate λ > 0
Output: Modified logits with dynamically filtered tail

1: // Phase 1: Calculate adaptive threshold from logit standard deviation
2: σ ← StandardDeviation(L)
3: amount_to_tighten ← S * (1 - Exp(-λ * σ))
4: t_adaptive ← 1.0 - amount_to_tighten

5: // Phase 2: Find the elbow in logit-space
6: Lsorted, Lidx ← Sort(L, descending=True)
7:
8: D1 ← Diff(Lsorted)
9: D2 ← |Diff(D1)|
10:
11: if Sum(D2) = 0 then return L end if // Handle linear logits
12:
13: D2norm ← D2 / Sum(D2)
14: CurvatureCDF ← CumulativeSum(D2norm)

15: // Phase 3: Filter, unsort, and return
16: mask_sorted ← CurvatureCDF > t_adaptive
17: mask_sorted ← Concatenate([False], mask_sorted, [True]) // Always keep top token
18:
19: Lsorted[mask_sorted] ← -∞
20: L ← Unsort(Lsorted, Lidx)
21:
22: return L