Na Zhu

Jia Zou, Xiaokai Zhang, Yiming He et al.

The human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdiscipline of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a neural-symbolic system, called FGeoDRL, to automatically perform human-like geometric deductive reasoning. The neural part is an AI agent based on reinforcement learning, capable of autonomously learning problem-solving methods from the feedback of a formalized environment, without the need for human supervision. It leverages a pre-trained natural language model to establish a policy network for theorem selection and employ Monte Carlo Tree Search for heuristic exploration. The symbolic part is a reinforcement learning environment based on geometry formalization theory and FormalGeo, which models GPS as a Markov Decision Process. In this formal symbolic system, the known conditions and objectives of the problem form the state space, while the set of theorems forms the action space. Leveraging FGeoDRL, we have achieved readable and verifiable automated solutions to geometric problems. Experiments conducted on the formalgeo7k dataset have achieved a problem-solving success rate of 86.40%. The project is available at https://github.com/PersonNoName/FGeoDRL.

Xiaokai Zhang, Yang Li, Na Zhu et al.

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.