A Probabilistic Inference Scaling Theory for LLM Self-Correction

• URL: http://arxiv.org/abs/2508.16456v1
• Date: Fri, 22 Aug 2025 15:15:38 GMT
• Title: A Probabilistic Inference Scaling Theory for LLM Self-Correction
• Authors: Zhe Yang, Yichang Zhang, Yudong Wang, Ziyao Xu, Junyang Lin, Zhifang Sui,
• Abstract summary: Large Language Models (LLMs) have demonstrated the capability to refine their generated answers through self-correction.<n>We propose a probabilistic theory to model the dynamics of accuracy change and explain the performance improvements observed in multi-round self-correction.
• Score: 49.42817548142699
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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: $Acc_t = Upp - \alpha^t(Upp - Acc_0),$ 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.

Related papers

• Decoupling the Effect of Chain-of-Thought Reasoning: A Human Label Variation Perspective [60.45433515408158]
  We show that long Chain-of-Thought (CoT) serves as a decisive decision-maker for the top option but fails to function as a granular distribution calibrator for ambiguous tasks.<n>We observe a distinct "decoupled mechanism": while CoT improves distributional alignment, final accuracy is dictated by CoT content.
  arXiv  Detail & Related papers  (2026-01-06T16:26:40Z)
• Beyond the Ideal: Analyzing the Inexact Muon Update [54.70108543057578]
  We show first analysis of the inexactized update at Muon's core.<n>We reveal a fundamental coupling between this inexactness and the optimal step size and momentum.
  arXiv  Detail & Related papers  (2025-10-22T18:01:07Z)
• Search-Based Correction of Reasoning Chains for Language Models [72.61861891295302]
  Chain-of-Thought (CoT) reasoning has advanced the capabilities and transparency of language models (LMs)<n>We introduce a new self-correction framework that augments each reasoning step in a CoT with a latent variable indicating its veracity.<n>We also introduce Search Corrector, a discrete search algorithm over-valued veracity assignments.
  arXiv  Detail & Related papers  (2025-05-17T04:16:36Z)
• Rejection via Learning Density Ratios [50.91522897152437]
  Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions.<n>We propose a different distributional perspective, where we seek to find an idealized data distribution which maximizes a pretrained model's performance.<n>Our framework is tested empirically over clean and noisy datasets.
  arXiv  Detail & Related papers  (2024-05-29T01:32:17Z)
• Just rotate it! Uncertainty estimation in closed-source models via multiple queries [3.8121150313479655]
  We propose a simple and effective method to estimate the uncertainty of closed-source deep neural network image classification models. We demonstrate significant improvements in the calibration of uncertainty estimates compared to the naive baseline of assigning 100% confidence to all predictions.
  arXiv  Detail & Related papers  (2024-05-22T17:45:38Z)
• CogDPM: Diffusion Probabilistic Models via Cognitive Predictive Coding [62.075029712357]
  This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM) CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and surface wind datasets.
  arXiv  Detail & Related papers  (2024-05-03T15:54:50Z)
• Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes [22.256068524699472]
  We introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes.<n>NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior.<n>We demonstrate that the bias introduced by our method can be controlled by multiplying the divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm.
  arXiv  Detail & Related papers  (2023-09-22T06:56:35Z)
• Ensemble Multi-Quantiles: Adaptively Flexible Distribution Prediction for Uncertainty Quantification [4.728311759896569]
  We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $mathbbP(mathbfy|mathbfX=x)$ in regression tasks. On extensive regression tasks from UCI datasets, we show that EMQ achieves state-of-the-art performance.
  arXiv  Detail & Related papers  (2022-11-26T11:45:32Z)
• Lassoed Tree Boosting [53.56229983630983]
  We prove that a gradient boosted tree algorithm with early stopping faster than $n-1/4$ L2 convergence in the large nonparametric space of cadlag functions of bounded sectional variation. Our convergence proofs are based on a novel, general theorem on early stopping with empirical loss minimizers of nested Donsker classes.
  arXiv  Detail & Related papers  (2022-05-22T00:34:41Z)
• Robustness and Accuracy Could Be Reconcilable by (Proper) Definition [109.62614226793833]
  The trade-off between robustness and accuracy has been widely studied in the adversarial literature. We find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty.
  arXiv  Detail & Related papers  (2022-02-21T10:36:09Z)
• Beyond the Mean-Field: Structured Deep Gaussian Processes Improve the Predictive Uncertainties [12.068153197381575]
  We propose a novel variational family that allows for retaining covariances between latent processes while achieving fast convergence. We provide an efficient implementation of our new approach and apply it to several benchmark datasets. It yields excellent results and strikes a better balance between accuracy and calibrated uncertainty estimates than its state-of-the-art alternatives.
  arXiv  Detail & Related papers  (2020-05-22T11:10:59Z)
• Estimation of Accurate and Calibrated Uncertainties in Deterministic models [0.8702432681310401]
  We devise a method to transform a deterministic prediction into a probabilistic one. We show that for doing so, one has to compromise between the accuracy and the reliability (calibration) of such a model. We show several examples both with synthetic data, where the underlying hidden noise can accurately be recovered, and with large real-world datasets.
  arXiv  Detail & Related papers  (2020-03-11T04:02:56Z)
• A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-$\ell_1$-Norm Interpolated Classifiers [3.167685495996986]
  This paper establishes a precise high-dimensional theory for boosting on separable data. Under a class of statistical models, we provide an exact analysis of the universality error of boosting. We also explicitly pin down the relation between the boosting test error and the optimal Bayes error.
  arXiv  Detail & Related papers  (2020-02-05T00:24:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.