MATHGLANCE: Multimodal Large Language Models Do Not Know Where to Look in Mathematical Diagrams

• URL: http://arxiv.org/abs/2503.20745v1
• Date: Wed, 26 Mar 2025 17:30:41 GMT
• Title: MATHGLANCE: Multimodal Large Language Models Do Not Know Where to Look in Mathematical Diagrams
• Authors: Yanpeng Sun, Shan Zhang, Wei Tang, Aotian Chen, Piotr Koniusz, Kai Zou, Yuan Xue, Anton van den Hengel,
• Abstract summary: Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements.<n>Current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether Multimodal Large Language Models genuinely understand mathematical diagrams beyond superficial pattern recognition.<n>We introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs.<n>We construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text annotated with geometric primitives and precise spatial relationships.
• Score: 65.02628814094639
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements. Unlike natural images, their inherently symbolic and abstract nature poses significant challenges for Multimodal Large Language Models (MLLMs). However, current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether MLLMs genuinely understand mathematical diagrams beyond superficial pattern recognition. To address this gap, we introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs. MATHGLANCE comprises 1.2K images and 1.6K carefully curated questions spanning four perception tasks: shape classification, object counting, relationship identification, and object grounding, covering diverse domains including plane geometry, solid geometry, and graphical representations. Our evaluation of MLLMs reveals that their ability to understand diagrams is notably limited, particularly in fine-grained grounding tasks. In response, we construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text pairs explicitly annotated with geometric primitives and precise spatial relationships. Training MLLM on GeoPeP leads to significant gains in perceptual accuracy, which in turn substantially improves mathematical reasoning. Our benchmark and dataset establish critical standards for evaluating and advancing multimodal mathematical understanding, providing valuable resources and insights to foster future MLLM research.

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