用符号系统生成几何题解,让大模型推理更准不乱说。
Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration
- 用符号逻辑自动构造几何题的分步解答路径
- 在几何推理基准上显著提升大模型准确率
- 适合需要严谨推理的数学/教育类AI研究者
多模态大语言模型(MLLM)在通用领域和多模态数学推理中取得显著进展,但在几何问题求解(GPS)方面仍面临挑战,主要由于缺乏精确的分步解题数据及推理过程中的严重幻觉。本文提出GeoGen,一个可自动生成几何图示分步推理路径的流水线。通过利用精确的符号推理,GeoGen构建了大规模高质量的问答对。为进一步增强MLLM的逻辑推理能力,我们使用GeoGen生成的合成数据训练了名为GeoLogic的大型语言模型(LLM)。GeoLogic作为自然语言与符号系统之间的桥梁,使符号工具能够验证MLLM输出,使推理过程更严谨,缓解幻觉问题。实验结果表明,该方法持续提升MLLM性能,在几何推理基准上取得显著成果。这一提升源于将大模型与符号系统优势融合,实现更可靠、可解释的几何问题求解方案。代码已开源:https://github.com/ycpNotFound/GeoGen。
原文摘要 · Abstract (English)
Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, \textbf{GeoGen} produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train \textbf{GeoLogic}, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.
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