Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey

2025/05/20 by Seunghyuk Cho, Cho, Seunghyuk, Z. Qin +9 · 2 citations
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computer Vision and Pattern Recognition (cs.CV) #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #Machine Learning (cs.LG) #Manufacturing Process and Optimization

paper · pdf · doi:10.48550/arxiv.2505.14340

openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Plane geometry problem solving (PGPS) has recently gained significant attention as a benchmark to assess the multi-modal reasoning capabilities of large vision-language models. Despite the growing interest in PGPS, the research community still lacks a comprehensive overview that systematically synthesizes recent work in PGPS. To fill this gap, we present a survey of existing PGPS studies. We first categorize PGPS methods into an encoder-decoder framework and summarize the corresponding output formats used by their encoders and decoders. Subsequently, we classify and analyze these encoders and decoders according to their architectural designs. Finally, we outline major challenges and promising directions for future research. In particular, we discuss the hallucination issues arising during the encoding phase within encoder-decoder architectures, as well as the problem of data leakage in current PGPS benchmarks.

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• GeoSketch: A Neural-Symbolic Approach to Geometric Multimodal Reasoning with Auxiliary Line Construction and Affine Transformation
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