E-GPS: Explainable Geometry Problem Solving via Top-Down Solver and Bottom-Up Generator

Geometry Problem Solving (GPS) has drawn growing attention recently due to its application prospects in intelligent education field. However, existing methods are still inadequate to meet the needs of practical application, suffering from the following limitations: 1) explainability is not ensured which is essential in real teaching scenarios; 2) the small scale and incomplete annotation of existing datasets make it hard for model to learn geometric knowledge. To tackle the above problems, we propose a novel method called Explainable Geometry Problem Solving (E-GPS). E-GPS first parses the geometric diagram and problem text into unified formal language representations. Then, the answer and explainable reasoning and solving steps are obtained by a Top-Down Problem Solver (TD-PS), which innovatively solves the problem from the target and focuses on what is needed. To alleviate the data issues, a Bottom-Up Problem Generator (BU-PG) is devised to augment the data set with various well-annotated constructed geometry problems. It enables us to train an enhanced theorem predictor with a better grasp of theorem knowledge, which further improves the efficiency of TD-PS. Extensive experiments demonstrate that E-GPS maintains comparable solving performances with fewer steps and provides outstanding explainability.