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.
