Language models solve complex geometry with symbolic reasoning
From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning
Artificial IntelligenceComputation and Language
Summary
Solving geometry problems is tough for AI because it needs both seeing a picture and doing math. The authors show that language models can solve difficult geometry tasks by first turning diagrams into symbols and then carefully reasoning through them. They test their method on a hard set of exam questions and find it matches the best systems while giving clear, step-by-step solutions. This approach helps reduce errors and makes the reasoning easier to follow.
What this means in practice
- •For math tutoring platforms: Generate clear step-by-step geometry solutions from student-submitted diagrams automatically.$Commercial implications: Enables developing AI-powered tutoring systems that provide interpretable geometry problem solving for students.
- •For educational software developers: Incorporate precise symbolic geometry reasoning engines to improve automated math problem verification.
Authors
Weichen Dai, Rafael Medeiros Cabral, Ziyi Shou, Yan Cao, Xin Shen, Dongcai Lu, Yi Zhou
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.