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

arXiv: https://arxiv.org/abs/2504.09440 · HTML: https://mlsanity.com/paper/2504.09440/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 19 of 19)

- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Lookback Lens: Detecting and Mitigating Contextual Hallucinations in Large Language Models Using Only Attention Maps](https://mlsanity.com/paper/2407.07071/) (2024)
- [Critique-out-Loud Reward Models](https://mlsanity.com/paper/2408.11791/) (2024)
- [TruthX: Alleviating Hallucinations by Editing Large Language Models in Truthful Space](https://mlsanity.com/paper/2402.17811/) (2024)
- [Halo: Estimation and Reduction of Hallucinations in Open-Source Weak Large Language Models](https://mlsanity.com/paper/2308.11764/) (2023)
- [DRT: Deep Reasoning Translation via Long Chain-of-Thought](https://mlsanity.com/paper/2412.17498/) (2024)
- [Constructing Benchmarks and Interventions for Combating Hallucinations in LLMs](https://mlsanity.com/paper/2404.09971/) (2024)
- [Mapping the Neuro-Symbolic AI Landscape by Architectures: A Handbook on Augmenting Deep Learning Through Symbolic Reasoning](https://mlsanity.com/paper/2410.22077/) (2024)
- [GloSoFarID: Global multispectral dataset for Solar Farm IDentification in satellite imagery](https://mlsanity.com/paper/2404.05180/) (2024)

## Built on by (most cited first, 13 of 13)

- [LLM-based Agents Suffer from Hallucinations: A Survey of Taxonomy, Methods, and Directions](https://mlsanity.com/paper/2509.18970/) (2025)
- [RoT: Enhancing Table Reasoning with Iterative Row-Wise Traversals](https://mlsanity.com/paper/2505.15110/) (2025)
- [Learning-at-Criticality in Large Language Models for Quantum Field Theory and Beyond](https://mlsanity.com/paper/2506.03703/) (2025)
- [ConfClip: Confidence-Weighted and Clipped Reward for Reinforcement Learning in LLMs](https://mlsanity.com/paper/2509.17730/) (2025)
- [Why Your Deep Research Agent Fails? On Hallucination Evaluation in Full Research Trajectory](https://mlsanity.com/paper/2601.22984/) (2026)
- [PRISM: Probing Reasoning, Instruction, and Source Memory in LLM Hallucinations](https://mlsanity.com/paper/2604.16909/) (2026)
- [SynPO: Synergizing Descriptiveness and Preference Optimization for Video Detailed Captioning](https://mlsanity.com/paper/2506.00835/) (2025)
- [OptArgus: A Multi-Agent System to Detect Hallucinations in LLM-based Optimization Modeling](https://mlsanity.com/paper/2605.11738/) (2026)
- [Do I Really Know? Learning Factual Self-Verification for Hallucination Reduction](https://mlsanity.com/paper/2602.02018/) (2026)
- [Reflective Confidence: Correcting Reasoning Flaws via Online Self-Correction](https://mlsanity.com/paper/2512.18605/) (2025)
- [Evaluating Large Language Models on Solved and Unsolved Problems in Graph Theory: Implications for Computing Education](https://mlsanity.com/paper/2602.05059/) (2026)
- [From Proof to Program: Characterizing Tool-Induced Reasoning Hallucinations in Large Language Models](https://mlsanity.com/paper/2511.10899/) (2025)
- [Magic, Madness, Heaven, Sin: LLM Output Diversity is Everything, Everywhere, All at Once](https://mlsanity.com/paper/2604.01504/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated strong mathematical reasoning capabilities but remain susceptible to hallucinations producing plausible yet incorrect statements especially in theorem proving, symbolic manipulation, and numerical computation. While self-consistency (SC) has been explored as a means to improve factuality in LLMs, existing approaches primarily apply SC to final-answer selection, neglecting the logical consistency of intermediate reasoning steps. In this work, we introduce a structured self-consistency framework designed to enhance the reliability of mathematical reasoning. Our method enforces self-consistency across intermediate steps and final outputs, reducing logical inconsistencies and hallucinations. We evaluate our approach across three core mathematical tasks: theorem proving, symbolic transformation, and numerical computation. Experimental results demonstrate that SC significantly improves proof validity, symbolic reasoning accuracy, and numerical stability while maintaining computational efficiency. Further analysis reveals that structured self-consistency not only enhances problem-solving accuracy but also reduces the variance of model-generated outputs. These findings highlight self-consistency as a robust mechanism for improving mathematical reasoning in LLMs, paving the way for more reliable and interpretable AI-driven mathematics.