2024/02/18 by Xiaokai Zhang, Yang Li, Zhang, Xiaokai +9 · 5 citations
Computer Science · Earth and Planetary Sciences · #Artificial Intelligence (cs.AI) #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #Geological Modeling and Analysis #Graph Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2402.11461
openalex publication_date 2024/02/18 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28
Geometric problem solving has always been a long-standing challenge in the fields of mathematical reasoning and artificial intelligence. We built a neural-symbolic system, called FGeo-HyperGNet, to automatically perform human-like geometric problem solving. The symbolic component is a formal system built on FormalGeo, which can automatically perform geometric relational reasoning and algebraic calculations and organize the solution into a hypergraph with conditions as hypernodes and theorems as hyperedges. The neural component, called HyperGNet, is a hypergraph neural network based on the attention mechanism, including an encoder to encode the structural and semantic information of the hypergraph and a theorem predictor to provide guidance in solving problems. The neural component predicts theorems according to the hypergraph, and the symbolic component applies theorems and updates the hypergraph, thus forming a predict-apply cycle to ultimately achieve readable and traceable automatic solving of geometric problems. Experiments demonstrate the effectiveness of this neural-symbolic architecture. We achieved state-of-the-art results with a TPA of 93.50% and a PSSR of 88.36% on the FormalGeo7K dataset. The code is available at https://github.com/BitSecret/HyperGNet.