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.

翻译：几何问题求解（GPS）一直是提升大型语言模型数学推理能力的核心挑战，因为它需要图解理解、符号操作和逻辑推理三者的结合。在现有文献中，研究者主要致力于同步图解描述与文本文字并求解问题。基于此思路，他们要么采用神经方法、符号方法，要么采用神经-符号方法。但这仅解决了前两个要求（即图解理解和符号操作），却使得逻辑推理发展不足——逻辑推理往往局限于单条思维链（CoT）。为弥补现有模型的这一缺陷，本文提出MARS-GPS，该方法生成多条并行推理路径，并通过Python代码执行进行数值验证，利用词元级熵作为置信度信号对推理路径排序，最终通过多阶段投票与自验证流程聚合答案。实验结果表明，采用8条并行推理路径的MARS-GPS在Geometry3K数据集上达到88.8%的准确率，较先前最优方法提升近11%；且随着推理路径数量从1增加到16，准确率持续提升（消融子集上提升6.0%）。我们在匿名仓库提供代码与数据：https://anonymous.4open.science/r/MARS-GPS-DE55。