GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912847803449344 |
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| author | Guo, Shasha Pang, Liang Wang, Xi Wang, Yanling Shen, Huawei Zhang, Jing |
| author_facet | Guo, Shasha Pang, Liang Wang, Xi Wang, Yanling Shen, Huawei Zhang, Jing |
| contents | Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation Guo, Shasha Pang, Liang Wang, Xi Wang, Yanling Shen, Huawei Zhang, Jing Computer Vision and Pattern Recognition Artificial Intelligence Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry. |
| title | GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence |
| url | https://arxiv.org/abs/2510.11020 |