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

Geometry Problem Solving has drawn growing attention recently due to its application prospects in intelligent ed-ucation field. However, existing methods are still inade-quate to meet the needs of practical application, suffering from the following limitations: 1) explainability is not en-sured which is essential in real teaching scenarios; 2) the small scale and incomplete annotation of existing datasets make it hard for model to comprehend geometric knowl-edge. 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 prob-lem 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 geome-try problems. It enables us to train an enhanced theorem predictor with a better grasp of theorem knowledge, which further improves the efficiency ofTD-PS. Extensive experi-ments demonstrate that E-GPS maintains comparable solving performances with fewer steps and provides outstanding explainability.

1. Introduction

Geometry Problem Solving (GPS) aims to obtain the an-swer of problem based on the given geometric diagram and textual problem description. It has drawn growing attention recently [4], [15], [22], [31] due to its application prospects in intelligent education field in high schools [2], [20]. Dif-ferent from general question answering (QA) tasks, GPS requires the model to possess the abilities of symbolic abstraction, logical reasoning and algebraic calculation simultaneously [6], [24], making it a challenging task even for large multimodal models (LMMs) like GPT-4V [37]. Therefore, recent works attempt to combine the procedural power of symbolic models with the general power of neural models. Among these, symbolic-based approaches [22], [25], [29], [32] first parse the geometric diagram and problem text into for-mal language representations, and then continuously pre-dict and apply predefined theorem rules to obtain the final answer. Neural-based approaches [4], [5], [4]0 tend to trans-fer the original problem into multi-modal features, and feed them into generative models to acquire an executable pro-gram sequence for an answer. However, they both suffer from the following two limitations which hinder their application in practical scenarios. Figure 1.

Output examples of two mainstream gps methods. case 1 and case 2 are chosen from inter-gps [22] and ngs [4], respectively. Content with red background is seen as inexplicable.