Towards Geometry Problem Solving in the Large Model Era: A Survey

2025-06-03

AI Summary

Geometric Problem Solving (GPS) has long suffered from automation bottlenecks due to its dual requirements of spatial understanding and rigorous logical reasoning, compounded by fragmented benchmarks, inconsistent evaluation protocols, and disjointed methodological approaches. To address these challenges, this work introduces the first unified 3D analytical framework for GPS tailored to the large-model era, spanning benchmark construction, multimodal (text-and-diagram) parsing, and reasoning paradigms. We propose an automated benchmark generation methodology and a novel interpretable neuro-symbolic reasoning approach that tightly integrates large language models, multimodal perception, symbolic reasoning, graph-structured modeling, and principled evaluation design. Our analysis systematically clarifies the field’s fragmentation, identifies fundamental technical bottlenecks, and delivers the first comprehensive roadmap for advancing geometric intelligence—enabling applications in education, computer-aided design (CAD), and computational geometry.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

Problem

• Automating geometry problem solving with AI
• Integrating spatial and logical reasoning challenges
• Unifying fragmented methodologies and benchmarks

Innovation

• Unified analytical paradigm for GPS
• Automated benchmark generation approach
• Interpretable neuro-symbolic integration method