From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning
TL;DR
It is demonstrated that a pure Large Language Model (LLM), when equipped with specialized modules, can rival state-of-the-art LMMs on complex geometry problems, and achieves performance comparable to Gemini 2.5 Pro while delivering clearer, human-like solutions.
Abstract
Plane geometry remains a significant challenge in AI, requiring the integration of visual perception and mathematical reasoning. While Large Multimodal Models (LMMs) naturally handle visuo-linguistic inputs, they are often computationally intensive and opaque. We demonstrate that a pure Large Language Model (LLM), when equipped with specialized modules, can rival state-of-the-art LMMs on complex geometry problems. Our framework integrates a Geometric Vision Parser, which translates diagrams into symbolic form, with a Symbolic Solver that performs formal deductions, thereby mitigating hallucinations and promoting interpretable reasoning. To enable rigorous evaluation, we curate a benchmark of challenging problems from the 2025 Chinese Zhongkao examinations, ensuring data novelty and testing deeper deductive skills. Experiments demonstrate that our approach achieves performance comparable to Gemini 2.5 Pro while delivering clearer, human-like solutions.
