A geometry problem solver based on heterogeneous graph

doi:10.1007/s10489-026-07471-z

A geometry problem solver based on heterogeneous graph

2026-09-22

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DOI：10.1007/s10489-026-07471-z

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Geometry Problem Solving (GPS) is a challenging multimodal task that requires understanding both textual descriptions and geometric diagrams to derive mathematical solutions. However, existing methods struggle to model diagram structural information, align textual symbols with visual primitives, and handle the sparse distribution of geometric primitives in the diagram. To address these limitations, we propose a novel geometry problem solver that models geometric diagrams as heterogeneous graphs to explicitly capture the structural relationships among geometric primitives. We first introduce a graph construction method that represents each diagram as a heterogeneous graph. Building on this, we present the Geometric Relation Heterogeneous Graph (Geo-RHG) dataset, which comprises geometric diagrams, corresponding textual descriptions, and their heterogeneous graph representations. To bridge the modality gap between text and diagrams, we employ a cross-modal pre-training strategy that explicitly aligns textual symbols with their corresponding visual primitives. We also develop a hierarchical fusion mechanism that incorporates structural cues into the visual features during the modality fusion stage. This integration enhances the model’s capacity to reason over geometric content and supports more accurate problem solving in multimodal contexts. Extensive experiments demonstrate that our approach achieves superior performance on GPS benchmarks, outperforming existing baselines in both accuracy and generalization. The dataset and code will be released at https://github.com/hzl7/GeoRHGraph upon publication.

Keywords:

Automatic problem solving

Heterogeneous graph

Multimodal

Feature representation

A geometry problem solver based on heterogeneous graph

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