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This research presents a framework where a pure Large Language Model, augmented with specialized symbolic modules, rivals multimodal systems on complex plane geometry tasks. By translating visual diagrams into symbolic form and performing formal deductions, the approach reduces hallucinations and offers interpretable reasoning without relying on computationally intensive vision encoders. The study validates this method against challenging benchmarks derived from 2025 Chinese high school exams, demonstrating that structured logical deduction can effectively guide language models in geometric contexts.
From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning
arXiv:2609.10335v1 Announce Type: new 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.
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.
Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
arXiv:2609.10335 [cs.AI]
(or arXiv:2609.10335v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.10335 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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