GNS: Solving Plane Geometry Problems by Neural-Symbolic Reasoning with Multi-Modal LLMs

With the outstanding capabilities of Large Language Models (LLMs), solving math word problems (MWP) has greatly progressed, achieving higher performance on several benchmark datasets. However, it is more challenging to solve plane geometry problems (PGPs) due to the necessity of understanding, reasoning and computation on two modality data including both geometry diagrams and textual questions, where Multi-Modal Large Language Models (MLLMs) have not been extensively explored. Previous works simply regarded a plane geometry problem as a multi-modal QA task, which ignored the importance of explicitly parsing geometric elements from problems. To tackle this limitation, we propose to solve plane Geometry problems by Neural-Symbolic reasoning with MLLMs (GNS). We first leverage an MLLM to understand PGPs through knowledge prediction and symbolic parsing, next perform mathematical reasoning to obtain solutions, and last adopt a symbolic solver to compute answers. Correspondingly, we introduce the largest PGPs dataset GNS-260K with multiple annotations including symbolic parsing, understanding, reasoning and computation. In experiments, our Phi3-Vision-based MLLM wins first place on the PGPs solving task of MathVista benchmark, outperforming GPT-4o, Gemini Ultra and other much larger MLLMs. While LLaVA-13B-based MLLM markedly exceeded other close-source and open-source MLLMs on the MathVerse benchmark and also achieved the new SOTA on GeoQA dataset.