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Theorem-Aware Geometry Problem Solving with Symbolic Reasoning and Theorem Prediction
Pan Lu · Ran Gong · Shibiao Jiang · Liang Qiu · Siyuan Huang · Xiaodan Liang · Song-Chun Zhu · Ran Gong

Geometry problem solving 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 \textit{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 is available at https://lupantech.github.io/inter-gps.

Author Information

Pan Lu (University of California, Los Angeles)
Ran Gong (UCLA)
Shibiao Jiang (Zhejiang University)
Liang Qiu (University of California, Los Angeles)

My name is Liang Qiu. I am doing research in the Center for Vision, Cognition, Learning, and Autonomy (VCLA) at UCLA. I design algorithms and write code to build multi-modal socially intelligent interactive systems. My research interests include natural language processing, dialogue management, computational sociology, and medical AI.

Siyuan Huang (University of California, Los Angeles)
Xiaodan Liang (Sun Yat-sen University)
Song-Chun Zhu (UCLA)
Ran Gong (University of California, Los Angeles)

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