A Probabilistic Inference Scaling Theory for LLM Self-Correction

2025-08-22

AI Summary

Prior work has not characterized how accuracy dynamically evolves during multi-turn self-correction in large language models (LLMs). Method: We propose the first probabilistic reasoning framework to formally model the convergence behavior of accuracy during self-correction, enabling prediction of the full performance improvement curve from a single correction step. Our approach integrates Bayesian inference with rigorous mathematical derivation. Contributions/Results: We systematically validate the framework across major LLMs—including GPT-4, Claude, and Llama—and diverse benchmarks (GSM8K, MMLU, HumanEval). Empirical results align closely with theoretical predictions (mean absolute error <2.1%), revealing for the first time an exponential convergence pattern in LLM self-correction. This provides a principled, interpretable, and quantifiable analytical paradigm for trustworthy AI—enabling both diagnostic insight and optimization guidance for iterative refinement strategies.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Modeling accuracy dynamics in LLM self-correction process
• Explaining performance improvements through probabilistic scaling theory
• Predicting multi-round accuracy curves from single-round data

Innovation

• Probabilistic theory models accuracy dynamics
• Predicts multi-round self-correction from single round
• Mathematical derivation defines convergence rate parameters