Papers › Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning
Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning
Pan Lu, Ran Gong, Shibiao Jiang, Liang Qiu, Siyuan Huang, Xiaodan Liang, Song-Chun Zhu
Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.
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Tasks
Datasets
Introduced by this paper, per the archive.
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Mathematical Question Answering | GeoS | Inter-GPS | Accuracy (%) | 67 | #1 of 2 | Archive leaderboard | report |
| Mathematical Question Answering | Geometry3K | Human Expert | Accuracy (%) | 90.9 | #1 of 8 | Archive leaderboard | report |
| Mathematical Question Answering | Geometry3K | Inter-GPS (GT) | Accuracy (%) | 78.3 | #2 of 8 | Archive leaderboard | report |
| Mathematical Question Answering | Geometry3K | Inter-GPS | Accuracy (%) | 57.5 | #6 of 8 | Archive leaderboard | report |
| Mathematical Question Answering | Geometry3K | Human | Accuracy (%) | 56.9 | #7 of 8 | Archive leaderboard | report |
| Mathematical Question Answering | Geometry3K | Random | Accuracy (%) | 25.0 | #8 of 8 | Archive leaderboard | report |
| Mathematical Reasoning | PGPS9K | Inter-GPS | Completion accuracy | 59.8 | #4 of 6 | Archive leaderboard | report |
| Scene Parsing | PGDP5K | Inter-GPS | Total Accuracy | 27.3 | #2 of 2 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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