AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning

TL;DR

AutoGPS introduces a neuro-symbolic framework that combines neural multimodal understanding with symbolic deductive reasoning to solve geometry problems reliably and interpretably, achieving state-of-the-art results.

Contribution

The paper presents AutoGPS, a novel neuro-symbolic system that formalizes geometry problems and performs rigorous deductive reasoning, improving reliability and interpretability over existing methods.

Findings

Achieves state-of-the-art performance on benchmark datasets.

99% logical coherence in human evaluations.

Provides minimal, human-readable solutions.

Abstract

Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories: neural-based and symbolic-based methods, both of which exhibit limitations in reliability and interpretability. To address this challenge, we propose AutoGPS, a neuro-symbolic collaborative framework that solves geometry problems with concise, reliable, and human-interpretable reasoning processes. Specifically, AutoGPS employs a Multimodal Problem Formalizer (MPF) and a Deductive Symbolic Reasoner (DSR). The MPF utilizes neural cross-modal comprehension to translate geometry problems into structured formal language representations, with feedback from DSR collaboratively. The DSR takes the formalization as input and formulates geometry problem solving as a hypergraph expansion task, executing mathematically rigorous and reliable derivation to produce minimal and human-readable stepwise solutions. Extensive experimental evaluations demonstrate that AutoGPS achieves state-of-the-art performance on benchmark datasets. Furthermore, human stepwise-reasoning evaluation confirms AutoGPS's impressive reliability and interpretability, with 99\% stepwise logical coherence.