@inproceedings{yang-etal-2025-probabilistic,
title = "A Probabilistic Inference Scaling Theory for {LLM} Self-Correction",
author = "Yang, Zhe and
Zhang, Yichang and
Wang, Yudong and
Xu, Ziyao and
Lin, Junyang and
Sui, Zhifang",
editor = "Christodoulopoulos, Christos and
Chakraborty, Tanmoy and
Rose, Carolyn and
Peng, Violet",
booktitle = "Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing",
month = nov,
year = "2025",
address = "Suzhou, China",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2025.emnlp-main.685/",
pages = "13584--13598",
ISBN = "979-8-89176-332-6",
abstract = "Large Language Models (LLMs) have demonstrated the capability to refine their generated answers through self-correction, enabling continuous performance improvement over multiple rounds. However, the mechanisms underlying how and why accuracy evolves during this iterative process remain unexplored. To fill this gap, we propose a probabilistic theory to model the dynamics of accuracy change and explain the performance improvements observed in multi-round self-correction. Through mathematical derivation, we establish that the accuracy after the $t^{th}$ round of self-correction is given by: $Acc_t = Upp - \alpha^t(Upp - Acc_0),$where $Acc_0$ denotes the initial accuracy, $Upp$ represents the upper bound of accuracy convergence, and $\alpha$ determines the rate of convergence. Based on our theory, these parameters can be calculated and the predicted accuracy curve then can be obtained through only a single round of self-correction. Extensive experiments across diverse models and datasets demonstrate that our theoretical predictions align closely with empirical accuracy curves, validating the effectiveness of the theory. Our work provides a theoretical foundation for understanding LLM self-correction, thus paving the way for further explorations."
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<abstract>Large Language Models (LLMs) have demonstrated the capability to refine their generated answers through self-correction, enabling continuous performance improvement over multiple rounds. However, the mechanisms underlying how and why accuracy evolves during this iterative process remain unexplored. To fill this gap, we propose a probabilistic theory to model the dynamics of accuracy change and explain the performance improvements observed in multi-round self-correction. Through mathematical derivation, we establish that the accuracy after the t^th round of self-correction is given by: Acc_t = Upp - α^t(Upp - Acc₀),where Acc₀ denotes the initial accuracy, Upp represents the upper bound of accuracy convergence, and α determines the rate of convergence. Based on our theory, these parameters can be calculated and the predicted accuracy curve then can be obtained through only a single round of self-correction. Extensive experiments across diverse models and datasets demonstrate that our theoretical predictions align closely with empirical accuracy curves, validating the effectiveness of the theory. Our work provides a theoretical foundation for understanding LLM self-correction, thus paving the way for further explorations.</abstract>
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%0 Conference Proceedings
%T A Probabilistic Inference Scaling Theory for LLM Self-Correction
%A Yang, Zhe
%A Zhang, Yichang
%A Wang, Yudong
%A Xu, Ziyao
%A Lin, Junyang
%A Sui, Zhifang
%Y Christodoulopoulos, Christos
%Y Chakraborty, Tanmoy
%Y Rose, Carolyn
%Y Peng, Violet
%S Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing
%D 2025
%8 November
%I Association for Computational Linguistics
%C Suzhou, China
%@ 979-8-89176-332-6
%F yang-etal-2025-probabilistic
%X Large Language Models (LLMs) have demonstrated the capability to refine their generated answers through self-correction, enabling continuous performance improvement over multiple rounds. However, the mechanisms underlying how and why accuracy evolves during this iterative process remain unexplored. To fill this gap, we propose a probabilistic theory to model the dynamics of accuracy change and explain the performance improvements observed in multi-round self-correction. Through mathematical derivation, we establish that the accuracy after the t^th round of self-correction is given by: Acc_t = Upp - α^t(Upp - Acc₀),where Acc₀ denotes the initial accuracy, Upp represents the upper bound of accuracy convergence, and α determines the rate of convergence. Based on our theory, these parameters can be calculated and the predicted accuracy curve then can be obtained through only a single round of self-correction. Extensive experiments across diverse models and datasets demonstrate that our theoretical predictions align closely with empirical accuracy curves, validating the effectiveness of the theory. Our work provides a theoretical foundation for understanding LLM self-correction, thus paving the way for further explorations.
%U https://aclanthology.org/2025.emnlp-main.685/
%P 13584-13598
Markdown (Informal)
[A Probabilistic Inference Scaling Theory for LLM Self-Correction](https://aclanthology.org/2025.emnlp-main.685/) (Yang et al., EMNLP 2025)
ACL