让大模型更懂几何题，精准捕捉局部关系与全局结构。
GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving
- 用13种几何理论模板自动识别关键局部特征
- 局部特征覆盖提升61%，全局建模速度加快20%
- 适合需要精确几何推理的数学教育与AI评测场景
几何问题求解仍是大型多模态模型（LMMs）的重大挑战，需兼顾全局形状识别与与几何理论相关的细微局部关系。为此，我们提出GeoFocus框架，包含两个核心模块：1）关键局部感知器，通过13种基于理论的感知模板自动识别并强调关键局部结构（如角度、平行线、相对距离），使关键局部特征覆盖率比此前方法提升61%；2）VertexLang，一种紧凑的拓扑形式语言，通过顶点坐标与连接关系编码全局图形。相比传统代码式编码，可减少20%的全局感知训练时间，同时提升拓扑识别准确率。在Geo3K、GeoQA和FormalGeo7K上评估，GeoFocus相较于领先专用模型提升4.7%准确率，并在多样视觉条件下展现出更强的鲁棒性，MATHVERSE测试表现优异。
原文摘要 · Abstract (English)
Geometry problem-solving remains a significant challenge for Large Multimodal Models (LMMs), requiring not only global shape recognition but also attention to intricate local relationships related to geometric theory. To address this, we propose GeoFocus, a novel framework comprising two core modules. 1) Critical Local Perceptor, which automatically identifies and emphasizes critical local structure (e.g., angles, parallel lines, comparative distances) through thirteen theory-based perception templates, boosting critical local feature coverage by 61% compared to previous methods. 2) VertexLang, a compact topology formal language, encodes global figures through vertex coordinates and connectivity relations. By replacing bulky code-based encodings, VertexLang reduces global perception training time by 20% while improving topology recognition accuracy. When evaluated in Geo3K, GeoQA, and FormalGeo7K, GeoFocus achieves a 4.7% accuracy improvement over leading specialized models and demonstrates superior robustness in MATHVERSE under diverse visual conditions. Project Page -- https://github.com/dle666/GeoFocus
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