AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning (2505.23381v1)

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.

• The paper introduces AutoGPS, a neuro-symbolic framework combining multimodal formalization and deductive reasoning to solve geometry problems with high reliability.
• AutoGPS achieved state-of-the-art performance on benchmark datasets, significantly outperforming leading MLLMs and demonstrating 99% stepwise logical coherence.
• This research highlights the potential of neuro-symbolic models for creating interpretable AI systems and advancing automated problem-solving tools for geometry.

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

The paper introduces AutoGPS, a neuro-symbolic framework designed to solve geometry problems by integrating multimodal formalization and deductive reasoning. This framework specifically addresses the limitations of existing neural-based and symbolic-based approaches, which often struggle with reliability and interpretability in geometry problem-solving.

Key Components and Methodology

AutoGPS consists of two main components: the Multimodal Problem Formalizer (MPF) and the Deductive Symbolic Reasoner (DSR). The MPF leverages neural cross-modal comprehension capabilities to translate geometry problems, including visual diagrams and textual descriptions, into structured formal language representations. This conversion process ensures that the problem's multimodal information is accurately captured and formalized. Meanwhile, the DSR executes geometry problem-solving as a hypergraph expansion task. By iterating over formalized inputs, it applies a rigorous process of deduction to derive human-readable, stepwise solutions.

Experimental Findings

The efficacy of AutoGPS is demonstrated through extensive evaluations on benchmark datasets, where it achieves state-of-the-art performance. Its solutions exhibit a high degree of logical coherence, with a 99% stepwise logical coherence highlighted during human evaluation. Notably, AutoGPS outperformed existing methods, including state-of-the-art multimodal LLMs (MLLMs), by a significant margin. For example, when compared to some of the leading MLLMs, AutoGPS showed improvements of 18% and 26.4% on two distinct datasets, respectively.

Practical and Theoretical Implications

Practically, AutoGPS represents a significant step forward in the development of automated tools for geometry problem-solving, offering reliable and interpretable solutions that are critical in educational and professional settings. Theoretically, it underscores the potential of neuro-symbolic models in bridging the gap between neural network capabilities and symbolic reasoning's precision. It challenges the AI community to further explore and refine the integration of symbolic and neural components to enhance the comprehension and problem-solving capabilities of AI systems.

Future Developments

Looking forward, AutoGPS opens avenues for more sophisticated neuro-symbolic models, particularly those capable of handling even more complex multimodal inputs and reasoning tasks. The advancement of such frameworks will rely heavily on continued research into multimodal alignment and the expansion of symbolic reasoning capabilities within AI systems. These developments could lead to more generalized AI applications that can perform a wide range of reasoning tasks with high reliability and interpretability, potentially transforming how AI is applied in fields that require rigorous problem-solving skills, such as mathematics and engineering.

In conclusion, the research presented in this paper marks an important advancement in AI-driven geometry problem-solving. AutoGPS not only outperforms existing approaches but also provides reliable, interpretable solutions that have significant implications for both theoretical research and practical applications.