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

ICLR 2026 Conference Submission17208 Authors

Keywords: AI for Math, Geometric Reasoning

Abstract:

Plane geometry is a long-standing challenge in AI, requiring the integration of visual perception and mathematical reasoning.
Large Multimodal Models (LMMs) such as Gemini 2.5 Pro handles visuo-linguistic inputs but are resource-intensive.
We show that a pure Large Language Model, 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 on angular relations, mitigating hallucinations and promoting interpretable reasoning.
To enable rigorous evaluation, we curate a benchmark of difficult problems from the 2025 Chinese Zhongkao examinations, ensuring 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.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 17208