---
title: "FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network"
authors:
  - "Xiaokai Zhang"
  - "Yang Li"
  - "Na Zhu"
  - "Cheng Qin"
  - "Zhenbing Zeng"
  - "Tuo Leng"
doi: "10.24963/ijcai.2025/527"
url: "https://ijcai.org/proceedings/2025/527"
pdf: "https://ijcai.org/proceedings/2025/0527.pdf"
venue: "Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"
year: 2025
pages: "4733-4741"
track: "Main Track"
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"
---

# FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network

Xiaokai Zhang, Yang Li, Na Zhu, Cheng Qin, Zhenbing Zeng, Tuo Leng

*Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence*, pages 4733-4741. DOI: [10.24963/ijcai.2025/527](https://doi.org/10.24963/ijcai.2025/527)

## 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.