@inproceedings{li-etal-2026-martingale,
title = "Martingale Foresight Sampling: A Principled Approach to Inference-Time {LLM} Decoding",
author = "Li, Huayu and
He, ZhengXiao and
Tian, Siyuan and
Wen, Jinghao and
Li, Ao",
editor = "Demberg, Vera and
Inui, Kentaro and
Marquez, Llu{\'i}s",
booktitle = "Proceedings of the 19th Conference of the {E}uropean Chapter of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = mar,
year = "2026",
address = "Rabat, Morocco",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.eacl-long.162/",
pages = "3522--3533",
ISBN = "979-8-89176-380-7",
abstract = "Standard autoregressive decoding in large language models (LLMs) is inherently short-sighted, often failing to find globally optimal reasoning paths due to its token-by-token generation process. While inference-time strategies like foresight sampling attempt to mitigate this by simulating future steps, they typically rely on ad-hoc heuristics for valuing paths and pruning the search space. This paper introduces Martingale Foresight Sampling (MFS), a principled framework that reformulates LLM decoding as a problem of identifying an optimal stochastic process. By modeling the quality of a reasoning path as a stochastic process, we leverage Martingale theory to design a theoretically-grounded algorithm. Our approach replaces heuristic mechanisms with principles from probability theory: step valuation is derived from the Doob Decomposition Theorem to measure a path{'}s predictable advantage, path selection uses Optional Stopping Theory for principled pruning of suboptimal candidates, and an adaptive stopping rule based on the Martingale Convergence Theorem terminates exploration once a path{'}s quality has provably converged. Experiments on six reasoning benchmarks demonstrate that MFS surpasses state-of-the-art methods in accuracy while significantly improving computational efficiency. Code will be released at \url{https://github.com/miraclehetech/EACL2026-Martingale-Foresight-Sampling}."
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<abstract>Standard autoregressive decoding in large language models (LLMs) is inherently short-sighted, often failing to find globally optimal reasoning paths due to its token-by-token generation process. While inference-time strategies like foresight sampling attempt to mitigate this by simulating future steps, they typically rely on ad-hoc heuristics for valuing paths and pruning the search space. This paper introduces Martingale Foresight Sampling (MFS), a principled framework that reformulates LLM decoding as a problem of identifying an optimal stochastic process. By modeling the quality of a reasoning path as a stochastic process, we leverage Martingale theory to design a theoretically-grounded algorithm. Our approach replaces heuristic mechanisms with principles from probability theory: step valuation is derived from the Doob Decomposition Theorem to measure a path’s predictable advantage, path selection uses Optional Stopping Theory for principled pruning of suboptimal candidates, and an adaptive stopping rule based on the Martingale Convergence Theorem terminates exploration once a path’s quality has provably converged. Experiments on six reasoning benchmarks demonstrate that MFS surpasses state-of-the-art methods in accuracy while significantly improving computational efficiency. Code will be released at https://github.com/miraclehetech/EACL2026-Martingale-Foresight-Sampling.</abstract>
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%0 Conference Proceedings
%T Martingale Foresight Sampling: A Principled Approach to Inference-Time LLM Decoding
%A Li, Huayu
%A He, ZhengXiao
%A Tian, Siyuan
%A Wen, Jinghao
%A Li, Ao
%Y Demberg, Vera
%Y Inui, Kentaro
%Y Marquez, Lluís
%S Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 March
%I Association for Computational Linguistics
%C Rabat, Morocco
%@ 979-8-89176-380-7
%F li-etal-2026-martingale
%X Standard autoregressive decoding in large language models (LLMs) is inherently short-sighted, often failing to find globally optimal reasoning paths due to its token-by-token generation process. While inference-time strategies like foresight sampling attempt to mitigate this by simulating future steps, they typically rely on ad-hoc heuristics for valuing paths and pruning the search space. This paper introduces Martingale Foresight Sampling (MFS), a principled framework that reformulates LLM decoding as a problem of identifying an optimal stochastic process. By modeling the quality of a reasoning path as a stochastic process, we leverage Martingale theory to design a theoretically-grounded algorithm. Our approach replaces heuristic mechanisms with principles from probability theory: step valuation is derived from the Doob Decomposition Theorem to measure a path’s predictable advantage, path selection uses Optional Stopping Theory for principled pruning of suboptimal candidates, and an adaptive stopping rule based on the Martingale Convergence Theorem terminates exploration once a path’s quality has provably converged. Experiments on six reasoning benchmarks demonstrate that MFS surpasses state-of-the-art methods in accuracy while significantly improving computational efficiency. Code will be released at https://github.com/miraclehetech/EACL2026-Martingale-Foresight-Sampling.
%U https://aclanthology.org/2026.eacl-long.162/
%P 3522-3533
Markdown (Informal)
[Martingale Foresight Sampling: A Principled Approach to Inference-Time LLM Decoding](https://aclanthology.org/2026.eacl-long.162/) (Li et al., EACL 2026)
ACL