用文本描述辅助线，提升视觉语言模型解几何题能力
GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation
- 将辅助线转化为结构化文本描述，避免代码生成依赖
- 通过跨模态奖励模型优化文本与图形的对齐效果
- 适用于需要空间推理的复杂立体几何问题求解
辅助线是解决复杂几何问题的关键，但对大型视觉语言模型（LVLM）仍具挑战。现有方法依赖代码驱动渲染生成辅助线，但在复杂立体几何场景中，其对精确代码的强依赖严重限制了鲁棒性。本文提出一种更简单稳定的方案：将辅助线构造表示为结构化文本描述。为弥合文本描述与空间结构之间的差距，设计了一种强化学习框架，核心为跨模态奖励模型，评估生成的辅助线描述与真实图示的匹配程度。该奖励信号驱动基于GRPO的强化学习阶段，生成更具信息量的辅助线描述。为支持训练与评估，构建了可扩展的数据流水线，并创建了包含3,018道真实考题的AuxSolidMath数据集，附带配对的图表与对齐的文本字段。基于此框架，提出GeoVLMath，一个用于求解复杂立体几何问题的LVLM。
原文摘要 · Abstract (English)
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.
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