# Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration

arXiv: https://arxiv.org/abs/2504.12773 · HTML: https://mlsanity.com/paper/2504.12773/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 21 of 21)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [InternVL: Scaling up Vision Foundation Models and Aligning for Generic Visual-Linguistic Tasks](https://mlsanity.com/paper/2312.14238/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [A Survey on Large Language Models for Recommendation](https://mlsanity.com/paper/2305.19860/) (2023)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Math-PUMA: Progressive Upward Multimodal Alignment to Enhance Mathematical Reasoning](https://mlsanity.com/paper/2408.08640/) (2024)
- [GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generation](https://mlsanity.com/paper/2406.11503/) (2024)
- [FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solving](https://mlsanity.com/paper/2310.18021/) (2023)
- [LANS: A Layout-Aware Neural Solver for Plane Geometry Problem](https://mlsanity.com/paper/2311.16476/) (2023)
- [GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training](https://mlsanity.com/paper/2412.11863/) (2024)
- [Plane Geometry Diagram Parsing](https://mlsanity.com/paper/2205.09363/) (2022)
- [PGDP5K: A Diagram Parsing Dataset for Plane Geometry Problems](https://mlsanity.com/paper/2205.09947/) (2022)
- [Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagram](https://mlsanity.com/paper/2407.07327/) (2024)
- [Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Process](https://mlsanity.com/paper/2405.06232/) (2024)

## Built on by (most cited first, 18 of 18)

- [THOR: Tool-Integrated Hierarchical Optimization via RL for Mathematical Reasoning](https://mlsanity.com/paper/2509.13761/) (2025)
- [Towards Geometry Problem Solving in the Large Model Era: A Survey](https://mlsanity.com/paper/2506.02690/) (2025)
- [Cognitive Mismatch in Multimodal Large Language Models for Discrete Symbol Understanding](https://mlsanity.com/paper/2603.18472/) (2026)
- [GeoSDF: Plane Geometry Diagram Synthesis via Signed Distance Field](https://mlsanity.com/paper/2506.13492/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [CircuitSense: A Hierarchical MLLM Benchmark Bridging Visual Comprehension and Symbolic Reasoning in Engineering Design Process](https://mlsanity.com/paper/2509.22339/) (2025)
- [GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning](https://mlsanity.com/paper/2603.22687/) (2026)
- [GenesisGeo: Technical Report](https://mlsanity.com/paper/2509.21896/) (2025)
- [Do Multi-Agents Solve Better Than Single? Evaluating Agentic Frameworks for Diagram-Grounded Geometry Problem Solving and Reasoning](https://mlsanity.com/paper/2512.16698/) (2025)
- [GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving](https://mlsanity.com/paper/2602.08524/) (2026)
- [GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagrams](https://mlsanity.com/paper/2603.19252/) (2026)
- [Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving](https://mlsanity.com/paper/2601.21164/) (2026)
- [A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning](https://mlsanity.com/paper/2603.08291/) (2026)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)
- [VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification](https://mlsanity.com/paper/2606.14176/) (2026)
- [AutoVSR: Automatic Visual-to-Symbolic Reasoning for Symbolic Expression Generation from Circuit Schematic](https://mlsanity.com/paper/2607.11338/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)
- [V-Rubrics: Visual Faithfulness via Rubric-Based Reinforcement Learning](https://mlsanity.com/paper/2608.25580/) (2026)

## Abstract (arXiv)

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, GeoGen produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train GeoLogic, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.