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Valid Stopping for LLM Generation via Empirical Dynamic Formal Lift

Sanjeda Akter, Ibne Farabi Shihab, Anuj Sharma

Abstract

We introduce Sequential-EDFL (Empirical Dynamic Formal Lift), applying anytime-valid sequential testing to language model generation stopping. Our approach tracks information lift -- the log-likelihood ratio between full models and deliberately weakened "skeleton" baselines -- using self-normalized empirical-Bernstein e-processes that provide formal delta-level error control regardless of stopping time. We handle unknown centering through online mean estimation, combine multiple parameters via mixture e-processes, and support adaptive resets under distributional drift. On six benchmarks, Sequential-EDFL reduces generation by 22-28% vs. sequential baselines while maintaining delta-level control with 12% computational overhead. We introduce automated skeletons (distilled submodels, randomized logits) and show robustness across skeleton families. Composing EDFL with a lightweight correctness gate (sentence boundaries + verifier) improves end-task correctness while preserving anytime-valid guarantees by only delaying stopping. Our certificates control information sufficiency, not factual correctness -- 10.9% of stopped sequences remain incorrect even with the gate (13.2-22.7% without it). EDFL serves as a first-stage filter reducing verification burden by 83%, not as a standalone solution for safety-critical domains.

Valid Stopping for LLM Generation via Empirical Dynamic Formal Lift

Abstract

We introduce Sequential-EDFL (Empirical Dynamic Formal Lift), applying anytime-valid sequential testing to language model generation stopping. Our approach tracks information lift -- the log-likelihood ratio between full models and deliberately weakened "skeleton" baselines -- using self-normalized empirical-Bernstein e-processes that provide formal delta-level error control regardless of stopping time. We handle unknown centering through online mean estimation, combine multiple parameters via mixture e-processes, and support adaptive resets under distributional drift. On six benchmarks, Sequential-EDFL reduces generation by 22-28% vs. sequential baselines while maintaining delta-level control with 12% computational overhead. We introduce automated skeletons (distilled submodels, randomized logits) and show robustness across skeleton families. Composing EDFL with a lightweight correctness gate (sentence boundaries + verifier) improves end-task correctness while preserving anytime-valid guarantees by only delaying stopping. Our certificates control information sufficiency, not factual correctness -- 10.9% of stopped sequences remain incorrect even with the gate (13.2-22.7% without it). EDFL serves as a first-stage filter reducing verification burden by 83%, not as a standalone solution for safety-critical domains.

Paper Structure

This paper contains 31 sections, 3 theorems, 7 equations, 4 figures, 20 tables.

Table of Contents

  1. Introduction
  2. Information Lift Framework
  3. Skeleton-Based Information Lift
  4. Skeleton Construction and Diagnostics
  5. Sequential E-Process Framework
  6. Experiments
  7. Main Results: Token Reduction with Formal Guarantees
  8. Discussion
  9. Related Work
  10. Conclusion
  11. Limitations
  12. Skeleton Details and Diagnostics
  13. Diagnostics checklist (used in all experiments).
  14. Automated Skeletons and Task-Agnostic Families
  15. Automated Skeleton Recipes
  16. ...and 16 more sections

Key Result

Theorem 3.1

Let $X_1, X_2, \ldots$ be information lift observations with $X_t \in [0, c]$. Using mixture e-process $M_t = \sum_{k=1}^K w_k M_t(\lambda_k)$ with threshold $u = 1/\delta$ and adaptive resets with budgets $\delta_j = 6\delta/(\pi^2 j^2)$, the stopping rule $\tau = \inf\{t: M_t \geq u\}$ satisfies: for any $\epsilon > 0$, where $\mu_s = \mathbb{E}[X_s | \mathcal{F}_{s-1}]$. This guarantee holds r

Figures (4)

  • Figure 1: Time-uniform empirical risk on GSM8K. Sequential-EDFL tracks target $\delta=0.1$ most closely.
  • Figure 2: Information lift: Full model $P$ (peaked) vs. skeleton $S$ (flat). Large lift indicates evidence accumulation.
  • Figure 3: Sequential-EDFL algorithm overview. Per-token: compute lift, update e-process, stop at boundary $u_J$, reset on drift.
  • Figure 4: Information sufficiency vs. factual correctness. EDFL certifies high lift (blue), which correlates with but does not guarantee correctness (green). The 16% gap (average across datasets) represents confident incorrect answers—our method's fundamental limitation for safety-critical deployment.

Theorems & Definitions (6)

  • Definition 2.1: Information Lift
  • Theorem 3.1: Anytime-Valid Information Sufficiency Certification
  • Lemma 3.2: Monotone delay preserves validity
  • Theorem 3.3: Validity with adaptive resets
  • Definition A.1: Clipped lift
  • proof