NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation

Obtaining large-scale, high-quality data with reasoning paths is crucial for improving the geometric reasoning capabilities of multi-modal large language models (MLLMs). However, existing data generation methods, whether based on predefined templates or constrained symbolic provers, inevitably face diversity and numerical generalization limitations. To address these limitations, we propose NeSyGeo, a novel neuro-symbolic framework for generating geometric reasoning data. First, we propose a domain-specific language grounded in the entity-relation-constraint paradigm to comprehensively represent all components of plane geometry, along with generative actions defined within this symbolic space. We then design a symbolic-visual-text pipeline that synthesizes symbolic sequences, maps them to corresponding visual and textual representations, and generates diverse question-answer (Q&A) pairs using large language models (LLMs). To the best of our knowledge, we are the first to propose a neuro-symbolic approach in generating multimodal reasoning data. Based on this framework, we construct NeSyGeo-CoT and NeSyGeo-Caption datasets, containing 100k samples, and release a new benchmark NeSyGeo-Test for evaluating geometric reasoning abilities in MLLMs. Experiments demonstrate that the proposal significantly and consistently improves the performance of multiple MLLMs under both reinforcement and supervised fine-tuning. With only 4k samples and two epochs of reinforcement fine-tuning, base models achieve improvements of up to +15.8% on MathVision, +8.4% on MathVerse, and +7.3% on GeoQA. Notably, a 4B model can be improved to outperform an 8B model from the same series on geometric reasoning tasks.

@article{wu2025_2505.17121,
  title={ NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation },
  author={ Weiming Wu and Zi-kang Wang and Jin Ye and Zhi Zhou and Yu-Feng Li and Lan-Zhe Guo },
  journal={arXiv preprint arXiv:2505.17121},
  year={ 2025 }
}