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

10 May 2021ACL 2021 5arXiv:2105.04165archive 2025-07-28

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

Arithmetic ReasoningGeometry Problem SolvingMathematical Question AnsweringMathematical ReasoningQuestion AnsweringScene ParsingSemantic ParsingVisual Question Answering (VQA)Visual Reasoning

Datasets

Introduced by this paper, per the archive.

Geometry3K

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
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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