A Probabilistic Inference Scaling Theory for LLM Self-Correction

摘要

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.