Problem
Research questions and friction points this paper is trying to address.
Geometric Problem Solving
Logical Inference
Chain-of-Thought
Large Language Models
Mathematical Reasoning
Beyond Symbolic Solving: Multi Chain-of-Thought Voting for Geometric Reasoning in Large Language Models
🤖 AI Summary
This work addresses the limitations of current large language models in geometric problem solving, which often rely on a single chain-of-thought and struggle to effectively integrate diagram understanding, symbolic manipulation, and multi-step logical reasoning. The authors propose MARS-GPS, a novel framework that introduces multi-chain-of-thought (Multi-CoT) voting with self-verification for geometric reasoning. It generates multiple parallel reasoning paths, validates numerical results via Python code execution, ranks paths using token-level entropy as a confidence measure, and aggregates answers through multi-stage voting. Evaluated on Geometry3K, the method achieves 88.8% accuracy—surpassing the previous state of the art by 11%—and demonstrates consistent performance gains of up to 6.0% as the number of parallel paths increases from 1 to 16, substantially overcoming the constraints of conventional neural or symbolic approaches.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Multi Chain-of-Thought
Geometric Reasoning
Token-level Entropy
Self-verification
Neuro-symbolic Integration
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