Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration
This work addresses geometry problem solving for AI systems, offering an incremental improvement by combining neural and symbolic methods to reduce hallucinations and enhance reliability.
The paper tackles the challenge of applying multimodal large language models (MLLMs) to geometry problem solving by proposing GeoGen, a pipeline that automatically generates step-wise reasoning paths and synthetic data, and GeoLogic, an LLM trained on this data to integrate symbolic tools, resulting in improved performance on geometric reasoning benchmarks.
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.