Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Process

TL;DR

This paper introduces DualGeoSolver, a dual-reasoning approach inspired by human cognition, which improves geometry problem solving by explicitly modeling both implicit knowledge retrieval and explicit reasoning steps.

Contribution

It proposes a novel dual-process framework for geometry problem solving that simulates human reasoning, combining knowledge retrieval and explicit inference in an iterative manner.

Findings

Outperforms existing methods on GeoQA and GeoQA+ datasets.

Shows improved accuracy and robustness in solving geometry problems.

Explicit modeling of human reasoning enhances problem-solving capabilities.

Abstract

Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge, and appropriately apply it in reasoning. However, existing works follow a paradigm of neural machine translation and only focus on enhancing the capability of encoders, which neglects the essential characteristics of human geometry reasoning. In this paper, inspired by dual-process theory, we propose a Dual-Reasoning Geometry Solver (DualGeoSolver) to simulate the dual-reasoning process of humans for GPS. Specifically, we construct two systems in DualGeoSolver, namely Knowledge System and Inference System. Knowledge System controls an implicit reasoning process, which is responsible for providing diagram information and geometry knowledge according to a step-wise reasoning goal generated by Inference System. Inference System conducts an explicit reasoning process, which specifies the goal in each reasoning step and applies the knowledge to generate program tokens for resolving it. The two systems carry out the above process iteratively, which behaves more in line with human cognition. We conduct extensive experiments on two benchmark datasets, GeoQA and GeoQA+. The results demonstrate the superiority of DualGeoSolver in both solving accuracy and robustness from explicitly modeling human reasoning process and knowledge application.