@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://preview.aclanthology.org/ingest-emnlp/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."
}