From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning
On the map: LLM reasoning → Spatial and embodied reasoning
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. Builds on 13 of its 20 references that are in the map. First posted on arXiv 9 Sep 2026.
Builds on
13 of 20 references.
Closest ancestors · 5
Same direction, newest first
- 2025GeometryZero: Advancing Geometry Solving via Group Contrastive Policy Optimization8 Jun
- 2025AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning29 May
- 2025NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation21 May
- 2023LANS: A Layout-Aware Neural Solver for Plane Geometry Problem25 Nov
- 2023A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram22 Feb
Other references · 8
- 2024YOLOv11: An Overview of the Key Architectural Enhancementscited by 425
- 2021GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoningcited by 228
- 2025Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2cited by 97
- 2025VisuoThink: Empowering LVLM Reasoning with Multimodal Tree Searchcited by 36
- 2023FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solvingcited by 27
- 2024GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-trainingcited by 23
- 2022Plane Geometry Diagram Parsingcited by 20
- 2025Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Informationcited by 10
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- 2026Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry
- 2025Euclid's Gift: Enhancing Spatial Perception and Reasoning in Vision-Language Models via Geometric Surrogate Tasks
- 2025GeoSketch: A Neural-Symbolic Approach to Geometric Multimodal Reasoning with Auxiliary Line Construction and Affine Transformation
- 2026GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning
- 2023GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning
- 2026ChitraMiti: Benchmarking Visual Grounding and Modality Reliance in Bengali Geometric Reasoning
- 2026Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning
- 2025CapGeo-Bench: Decoupling Visual Perception from Reasoning and Evaluating Geometric Understanding