GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation

• URL: http://arxiv.org/abs/2510.11020v1
• Date: Mon, 13 Oct 2025 05:33:51 GMT
• Title: GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation
• Authors: Shasha Guo, Liang Pang, Xi Wang, Yanling Wang, Huawei Shen, Jing Zhang,
• Abstract summary: We present GeoVLMath, an open-source LVLM tailored to auxiliary-line reasoning in solid geometry.<n>We generate textual descriptions of auxiliary-line constructions to better align with the representational strengths of LVLMs.<n>Built on this reward, we present GeoVLMath, an open-source LVLM tailored to auxiliary-line reasoning in solid geometry.
• Score: 54.53486231309254
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Rather than editing diagrams to draw auxiliary lines, which current image editing models struggle to render with geometric precision, we generate textual descriptions of auxiliary-line constructions to better align with the representational strengths of LVLMs. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. At the core of our approach is a cross-modal reward that evaluates how well the generated auxiliary-line description for an original diagram matches a ground-truth auxiliary-line diagram. Built on this reward, we present GeoVLMath, an open-source LVLM tailored to auxiliary-line reasoning in solid geometry. This fine-grained signal drives a GRPO-based RL stage, yielding precise diagram-text alignment. To support training, we develop a scalable data creation pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. At the 3B and 7B scales, GeoVLMath achieves competitive and often superior performance compared with strong open-source and proprietary LVLMs on auxiliary-line reasoning benchmarks.

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