# Anytime-Valid Answer Sufficiency Certificates for LLM Generation via Sequential Information Lift

arXiv: https://arxiv.org/abs/2510.06478 · HTML: https://mlsanity.com/paper/2510.06478/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 58 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 30 of 38)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Wizard of Wikipedia: Knowledge-Powered Conversational agents](https://mlsanity.com/paper/1811.01241/) (2018)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Lexically Constrained Decoding for Sequence Generation Using Grid Beam Search](https://mlsanity.com/paper/1704.07138/) (2017)
- [ASQA: Factoid Questions Meet Long-Form Answers](https://mlsanity.com/paper/2204.06092/) (2022)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation](https://mlsanity.com/paper/2307.03987/) (2023)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)

## Built on by (most cited first, 3 of 3)

- [EST-PRM: Stress-Testing Process Reward Models Before They Become Load-Bearing](https://mlsanity.com/paper/2606.00437/) (2026)
- [Continual Calibration: Coverage Can Collapse Before Accuracy in Lifelong LLM Fine-Tuning](https://mlsanity.com/paper/2604.23987/) (2026)
- [Private Anytime Selective-Risk Certification for Federated Retrieval-Augmented Generation: Guarantees and Empirical Limits](https://mlsanity.com/paper/2608.07913/) (2026)

## Abstract (arXiv)

We introduce Sequential-EDFL (Empirical Dynamic Formal Lift), which applies anytime-valid sequential testing to language model generation stopping. Our approach tracks information lift, defined as the log-likelihood ratio between the full model and deliberately weakened "skeleton" baselines, using self-normalized empirical-Bernstein e-processes that provide formal delta-level error control regardless of stopping time. This delta guarantee controls premature stopping when information lift is insufficient relative to the skeleton, and it does not imply delta control of factual incorrectness or hallucinations. 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 length by 22 to 28 percent relative to sequential baselines while maintaining delta-level control with 12 percent computational overhead. We introduce automated skeletons (distilled submodels and randomized logits) and show robustness across skeleton families. Composing EDFL with a lightweight correctness gate (sentence boundaries plus a verifier) improves end-task correctness while preserving anytime-valid guarantees by only delaying stopping. Our certificates control information sufficiency, not factual correctness. Specifically, 10.9 percent of stopped sequences remain incorrect even with the gate (13.2 to 22.7 percent without it). EDFL serves as a first-stage filter that can reduce verification burden: when applied to stopped sequences, the gate validates 83 percent of stops, requiring full verification only for the remaining 17 percent, plus all non-stopped sequences. EDFL is not a standalone solution for safety-critical domains.