# A Probabilistic Inference Scaling Theory for LLM Self-Correction

arXiv: https://arxiv.org/abs/2508.16456 · HTML: https://mlsanity.com/paper/2508.16456/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 42 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Builds on (most cited first, 30 of 33)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Language Models can Solve Computer Tasks](https://mlsanity.com/paper/2303.17491/) (2023)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Planning with Large Language Models for Code Generation](https://mlsanity.com/paper/2303.05510/) (2023)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Can Large Language Models Really Improve by Self-critiquing Their Own Plans?](https://mlsanity.com/paper/2310.08118/) (2023)
- [GPT-4 Doesn't Know It's Wrong: An Analysis of Iterative Prompting for Reasoning Problems](https://mlsanity.com/paper/2310.12397/) (2023)
- [Small Language Models Need Strong Verifiers to Self-Correct Reasoning](https://mlsanity.com/paper/2404.17140/) (2024)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Don't throw away your value model! Generating more preferable text with Value-Guided Monte-Carlo Tree Search decoding](https://mlsanity.com/paper/2309.15028/) (2023)
- [Large Language Models have Intrinsic Self-Correction Ability](https://mlsanity.com/paper/2406.15673/) (2024)
- [Self-Polish: Enhance Reasoning in Large Language Models via Problem Refinement](https://mlsanity.com/paper/2305.14497/) (2023)
- [Understanding the Dark Side of LLMs' Intrinsic Self-Correction](https://mlsanity.com/paper/2412.14959/) (2024)

## Built on by (most cited first, 9 of 9)

- [MemoryBench: A Benchmark for Memory and Continual Learning in LLM Systems](https://mlsanity.com/paper/2510.17281/) (2025)
- [Self-Correction as Feedback Control: Error Dynamics, Stability Thresholds, and Prompt Interventions in LLMs](https://mlsanity.com/paper/2604.22273/) (2026)
- [Verify, Repair, Repeat, or Stop? Robust Stopping for Noisy Verify-Repair Loops in LLM Agents](https://mlsanity.com/paper/2607.17641/) (2026)
- [Towards Better RL Training Data Utilization via Second-Order Rollout](https://mlsanity.com/paper/2602.22765/) (2026)
- [Synergizing Discriminative Exemplars and Self-Refined Experience for MLLM-based In-Context Learning in Medical Diagnosis](https://mlsanity.com/paper/2603.27737/) (2026)
- [Correction and Corruption: A Two-Rate View of Error Flow in LLM Protocols](https://mlsanity.com/paper/2604.18245/) (2026)
- [Understanding Scattered Forest Search: A Version-Space Perspective on Multi-Turn Program Correction](https://mlsanity.com/paper/2604.23989/) (2026)
- [Long-Horizon Scaling: How Model Capabilities Shape the Returns to Computation](https://mlsanity.com/paper/2609.35236/) (2026)
- [Pay for the Fault, Not the Flow: Label-Free In-Flow Multi-Agent Workflow Optimization](https://mlsanity.com/paper/2610.01017/) (2026)

## Abstract (arXiv)

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 tth round of self-correction is given by: Acct = Upp - αt(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.