Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Believe Your Model: Distribution-Guided Confidence Calibration

Xizhong Yang, Haotian Zhang, Huiming Wang, Mofei Song

TL;DR

DistriVoting is proposed, which incorporates distributional priors as another signal alongside confidence during voting to mitigate overlap between the two distributions and significantly outperforms state-of-the-art approaches.

Abstract

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer. While prior work has analyzed that internal model signals like confidence scores can partly indicate response correctness and exhibit a distributional correlation with accuracy, such distributional information has not been fully utilized to guide answer selection. Motivated by this, we propose DistriVoting, which incorporates distributional priors as another signal alongside confidence during voting. Specifically, our method (1) first decomposes the mixed confidence distribution into positive and negative components using Gaussian Mixture Models, (2) then applies a reject filter based on positive/negative samples from them to mitigate overlap between the two distributions. Besides, to further alleviate the overlap from the perspective of distribution itself, we propose SelfStepConf, which uses step-level confidence to dynamically adjust inference process, increasing the separation between the two distributions to improve the reliability of confidences in voting. Experiments across 16 models and 5 benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches.

Believe Your Model: Distribution-Guided Confidence Calibration

TL;DR

DistriVoting is proposed, which incorporates distributional priors as another signal alongside confidence during voting to mitigate overlap between the two distributions and significantly outperforms state-of-the-art approaches.

Abstract

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer. While prior work has analyzed that internal model signals like confidence scores can partly indicate response correctness and exhibit a distributional correlation with accuracy, such distributional information has not been fully utilized to guide answer selection. Motivated by this, we propose DistriVoting, which incorporates distributional priors as another signal alongside confidence during voting. Specifically, our method (1) first decomposes the mixed confidence distribution into positive and negative components using Gaussian Mixture Models, (2) then applies a reject filter based on positive/negative samples from them to mitigate overlap between the two distributions. Besides, to further alleviate the overlap from the perspective of distribution itself, we propose SelfStepConf, which uses step-level confidence to dynamically adjust inference process, increasing the separation between the two distributions to improve the reliability of confidences in voting. Experiments across 16 models and 5 benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches.
Paper Structure (69 sections, 3 theorems, 34 equations, 17 figures, 25 tables, 3 algorithms)

This paper contains 69 sections, 3 theorems, 34 equations, 17 figures, 25 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Confidence of Trajectory
  4. Distribution of Confidence
  5. Distributions Distance and Voting Accuracy
  6. Methodology
  7. Overview
  8. SelfStepConf
  9. Reflection Trigger.
  10. Reflection Injection.
  11. Distribution Voting
  12. GMM Modeling.
  13. GMM Filter.
  14. Reject Filter.
  15. Hierarchical Voting.
  16. ...and 54 more sections

Key Result

Theorem 2.1

Let $f(x) = \frac{1}{\sqrt{2\pi\sigma_1^2}} \exp\left(-\frac{(x-\mu_1)^2}{2\sigma_1^2}\right)$ and $g(x) = \frac{1}{\sqrt{2\pi\sigma_2^2}} \exp\left(-\frac{(x-\mu_2)^2}{2\sigma_2^2}\right)$ be the probability density functions of normal distributions with means $\mu_1, \mu_2$ and variances $\sigma_1 when $\mu_1 \neq \mu_2$, $R(\mu_1, \mu_2)$ is strictly monotonically increasing with respect to $\d

Figures (17)

  • Figure 1: Overview of DistriVoting. First model the original distribution using GMM, then filter out negative samples, finally reject false positives from the positive distribution.
  • Figure 2: Confidence distribution (HMMT2025) via DeepSeek-R1-8B, sampling 512 trajectories/query. Up: Confidence frequency histogram; Down: Accuracy curves for positive/negative intervals. Complete results are provided in \ref{['tab:appendix_complete_ssc_distribution']} of \ref{['sec:appendix_complete_ssc_distribution']}.
  • Figure 3: Optimal top-threshold traversal results using Qwen3-8B, sampling 256 responses/question (64 repeats). Complete results are provided in \ref{['fig:appendix_complete_top50_analysis']} of \ref{['sec:appendix_complete_top50_analysis']}.
  • Figure 4: Visualizing answer distribution as Gaussian components in GMM using DeepSeek-R1-8B, sampling 512 responses/query on HMMT2025. Complete results provided in \ref{['fig:appendix_complete_gmm_components_analysis']} of \ref{['sec:appendix_complete_gmm_components_analysis']}.
  • Figure 5: Comparing trajectory-level confidence between SSC and BasicInference using Qwen3-14B-NonThinking, sampling 512 responses/query. Complete results provided in \ref{['fig:appendix_complete_trajlevel_conf_analysis']} of \ref{['sec:appendix_complete_trajlevel_conf_analysis']}.
  • ...and 12 more figures

Theorems & Definitions (6)

  • Theorem 2.1
  • Theorem 2.2
  • proof
  • Corollary B.1
  • Remark B.2
  • proof