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.

The programming skill is one crucial ability for Large Language Models (LLMs), necessitating a deep understanding of programming languages (PLs) and their correlation with natural languages (NLs). We examine the impact of pre-training data on code-focused LLMs’ performance by assessing the comment density as a measure of PL-NL alignment. Given the scarcity of code-comment aligned data in pre-training corpora, we introduce a novel data augmentation method that generates comments for existing code, coupled with a data filtering strategy that filters out code data poorly correlated with natural language. We conducted experiments on three code-focused LLMs and observed consistent improvements in performance on two widely-used programming skill benchmarks. Notably, the model trained on the augmented data outperformed both the model used for generating comments and the model further trained on the data without augmentation.