Title: GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Cross-Modal Reward, Geometry Reasoning, Auxiliary Lines Creation, Solid Geometry

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 opensource and proprietary LVLMs on auxiliary-line reasoning benchmarks.

TL;DR: We introduce a cross-modal reward that aligns textual auxiliary-line descriptions with diagrams, driving GRPO-based training of GeoVLMath (3B/7B) on our AuxSolidMath dataset.