From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning

2026-09-09

AI Summary

研究通过结合几何视觉解析器和符号求解器，使大型语言模型能够处理复杂的几何推理问题，减少了计算强度并提高了可解释性。

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.

Problem

• Plane Geometry
• AI
• Visual Perception
• Mathematical Reasoning
• Large Multimodal Models

Innovation

• Geometric Vision Parser
• Symbolic Solver
• Large Language Model (LLM)
• Interpretable Reasoning