Enhancing Mathematical Reasoning in Large Language Models with Self-Consistency-Based Hallucination Detection

MingShan Liu, Shi Bo, Jialing Fang·April 13, 2025

Summary

A self-consistency framework enhances large language models' reliability in mathematical reasoning by ensuring logical consistency across steps and outputs. Evaluated across theorem proving, symbolic transformation, and numerical computation, this method significantly improves accuracy and consistency, making LLMs more reliable for high-precision mathematical tasks. Structured self-consistency maintains computational efficiency, addressing the trade-off between reasoning accuracy and inference cost. Recent research adapts self-consistency for open-ended tasks through response clustering and iterative refinement, enhancing applicability and factual reliability. The proposed approach, without requiring architectural changes, specifically targets mathematical reasoning tasks, improving consistency and balancing accuracy with efficiency.

Introduction
Background
Overview of large language models (LLMs) and their applications in mathematical reasoning
Challenges in ensuring logical consistency in LLM outputs
Objective
To present a self-consistency framework that improves the reliability of LLMs in mathematical tasks
Method
Theoretical Foundation
Explanation of self-consistency principles and their relevance to mathematical reasoning
Framework Components
Overview of the self-consistency framework structure
Detailed description of each component (e.g., logical consistency checks, iterative refinement)
Evaluation Across Tasks
Description of the evaluation process across theorem proving, symbolic transformation, and numerical computation
Presentation of results and improvements in accuracy and consistency
Computational Efficiency
Discussion on how the framework maintains computational efficiency while enhancing reasoning accuracy
Adaptation for Open-Ended Tasks
Response Clustering
Explanation of response clustering techniques and their role in enhancing applicability
Iterative Refinement
Description of iterative refinement methods for improving factual reliability in open-ended tasks
Application and Results
Case Studies
Presentation of case studies demonstrating the framework's effectiveness in real-world mathematical reasoning tasks
Comparative Analysis
Comparison of the proposed framework with existing methods in terms of accuracy, consistency, and computational cost
Proposed Approach
Targeted Improvements
Explanation of how the framework specifically targets mathematical reasoning tasks
Balancing Accuracy and Efficiency
Discussion on how the framework achieves a balance between reasoning accuracy and computational efficiency
Conclusion
Future Directions
Suggestions for further research and development in self-consistency frameworks for LLMs
Impact and Significance
Summary of the framework's impact on the reliability and applicability of LLMs in mathematical reasoning
Basic info
papers
artificial intelligence
Advanced features