A Probabilistic Inference Scaling Theory for LLM Self-Correction

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 - Acc 0 ), where Acc 0 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.