{"type":"ScholarlyArticle","title":"FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network","authors":[{"name":"Xiaokai Zhang","slug":"xiaokai-zhang","given":"Xiaokai","family":"Zhang","affiliation":""},{"name":"Yang Li","slug":"yang-li","given":"Yang","family":"Li","affiliation":""},{"name":"Na Zhu","slug":"na-zhu","given":"Na","family":"Zhu","affiliation":""},{"name":"Cheng Qin","slug":"cheng-qin","given":"Cheng","family":"Qin","affiliation":""},{"name":"Zhenbing Zeng","slug":"zhenbing-zeng","given":"Zhenbing","family":"Zeng","affiliation":""},{"name":"Tuo Leng","slug":"tuo-leng","given":"Tuo","family":"Leng","affiliation":""}],"abstract":"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 effectively 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 correctness and 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.","doi":"10.24963/ijcai.2025/527","url":"https://ijcai.org/proceedings/2025/527","pdf":"https://ijcai.org/proceedings/2025/0527.pdf","markdown":"https://ijcai.org/proceedings/2025/527.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/527","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":527,"pages":{"first":4733,"last":4741},"keywords":["Knowledge Representation and Reasoning: KRR: Learning and reasoning","Machine Learning: ML: Supervised Learning","Search: S: Heuristic search","Knowledge Representation and Reasoning: KRR: Automated reasoning and theorem proving"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}