Beyond Symbolic Solving: Multi Chain-of-Thought Voting for Geometric Reasoning in Large Language Models

TL;DR

This paper introduces MARS-GPS, a multi-chain reasoning approach with voting and verification, significantly improving geometric reasoning accuracy in large language models.

Contribution

It proposes a novel multi-chain-of-thought voting method with parallel rollouts and code verification, advancing logical inference in geometric problem solving.

Findings

Achieves 88.8% accuracy on Geometry3K, surpassing previous state-of-the-art.

Accuracy improves with more rollouts, up to 16, with a +6.0% gain.

Multi-chain reasoning with voting enhances logical inference in LLMs.

Abstract

Geometric Problem Solving (GPS) remains at the heart of enhancing mathematical reasoning in large language models because it requires the combination of diagrammatic understanding, symbolic manipulation and logical inference. In existing literature, researchers have chiefly focused on synchronising the diagram descriptions with text literals and solving the problem. In this vein, they have either taken a neural, symbolic or neuro-symbolic approach. But this solves only the first two of the requirements, namely diagrammatic understanding and symbolic manipulation, while leaving logical inference underdeveloped. The logical inference is often limited to one chain-of-thought (CoT). To address this weakness in hitherto existing models, this paper proposes MARS-GPS, that generates multiple parallel reasoning rollouts augmented with Python code execution for numerical verification, ranks them using token-level entropy as a confidence signal, and aggregates answers through a multi-stage voting and self-verification pipeline. Empirical results show that MARS-GPS with 8 parallel rollouts achieves 88.8% on Geometry3K, a nearly +11% improvement over the prior state-of-the-art, with accuracy scaling consistently as the number of rollouts increases from 1 to 16 (+6.0% on ablation subset). We provide our code and data in an anonymous repository: https://anonymous.4open.science/r/MARS-GPS-DE55.