Geometry Problem Solving Based on Counter-Factual Evolutionary Reasoning

As a representative topic in natural language processing and automated theorem proving, geometry problem solving requires an abstract problem understanding and symbolic reasoning. A major challenge here is to find a feasible reasoning sequence that is consistent with given axioms and the theorems already proved. Most recent methods have exploited neural network-based techniques to automatically discover eligible solving steps. Such a kind of methods, however, is greatly impacted by the expert solutions for training. To improve the accuracy, this paper proposes a new method called counterfactual evolutionary reasoning, which uses a generative adversarial network to generate initial reasoning sequences and then introduces counterfactual reasoning to explore potential solutions. By directly exploring theorem candidates rather than the neural network selection, the new method can sufficiently extend the searching space to get a more appropriate reasoning step. Through comparative experiments on the recent proposed Geometry3k, the largest geometry problem solving dataset, our method generally achieves a higher accuracy than most previous methods, bringing an overall improvement about 4.4% compared with the transformer models.