Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagram

TL;DR

This paper introduces PGPSNet-v2, a neural-symbolic model for geometry problem solving that fuses diagram and text, employs explicit reasoning, and verifies solutions to improve accuracy and explainability.

Contribution

The paper presents a novel neural-symbolic approach with a multi-step process including modal fusion, explicit reasoning, and solution verification for geometry problem solving.

Findings

Outperforms existing symbolic and neural solvers on Geometry3K and PGPS9K datasets.

Achieves better accuracy while maintaining explainability.

Effective components include modal fusion, explicit reasoning, and multi-level verification.

Abstract

Geometry problem solving (GPS) requires capacities of multi-modal understanding, multi-hop reasoning and theorem knowledge application. In this paper, we propose a neural-symbolic model for plane geometry problem solving (PGPS), named PGPSNet-v2, with three key steps: modal fusion, reasoning process and knowledge verification. In modal fusion, we leverage textual clauses to express fine-grained structural and semantic content of geometry diagram, and fuse diagram with textual problem efficiently through structural-semantic pre-training. For reasoning, we design an explicable solution program to describe the geometric reasoning process, and employ a self-limited decoder to generate solution program autoregressively. To reduce solution errors, a multi-level theorem verifier is proposed to eliminate solutions that do not match geometric principles, alleviating the hallucination of the neural model. We also construct a large-scale geometry problem dataset called PGPS9K, containing fine-grained annotations of textual clauses, solution program and involved knowledge tuples. Extensive experiments on datasets Geometry3K and PGPS9K show that our PGPSNet solver outperforms existing symbolic and neural solvers in GPS performance, while maintaining good explainability and reliability, and the solver components (fusion, reasoning, verification) are all justified effective.