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

2025-05-29

AI Summary

Geometric problem solving demands both multimodal understanding and rigorous mathematical reasoning, yet existing neural or symbolic approaches suffer from limitations in reliability and interpretability. This paper proposes a neuro-symbolic collaborative framework featuring a novel closed-loop interaction between a multimodal problem formalizer and a deductive symbolic solver, modeling geometric reasoning as a hypergraph expansion task. The framework integrates vision-language cross-modal comprehension, formal language compilation, symbolic deduction, and feedback-driven formalization refinement to generate minimal, human-readable proof steps. It achieves state-of-the-art performance across multiple benchmarks. Human evaluation confirms logical consistency in 99% of generated reasoning steps, demonstrating substantial improvements in both reliability and interpretability.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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. The project homepage is at https://jayce-ping.github.io/AutoGPS-homepage.

Problem

• Automated geometry problem solving via multimodal formalization
• Neuro-symbolic framework for reliable, interpretable reasoning
• Hypergraph expansion for rigorous, human-readable stepwise solutions

Innovation

• Neuro-symbolic framework for geometry problem solving
• Multimodal formalization with neural cross-modal comprehension
• Deductive hypergraph expansion for reliable reasoning