GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving

TL;DR

GeoFocus introduces a dual-module framework that enhances geometric reasoning in multimodal models by focusing on critical local structures and efficient global topology encoding, significantly improving accuracy and robustness.

Contribution

The paper presents GeoFocus, a novel approach combining theory-based local perception and a compact topology language to improve geometric problem-solving in multimodal models.

Findings

61% increase in critical local feature coverage

20% reduction in global perception training time

4.7% accuracy improvement over state-of-the-art models

Abstract

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