GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation
Yuan Feng, Yue Yang, Xiaohan He, Jiatong Zhao, Jianlong Chen, Daocheng Fu, Qi Liu, Renqiu Xia
Abstract
Geometric problem solving constitutes a critical branch of mathematical reasoning, requiring precise analysis of shapes and spatial relationships. Current evaluations of geometric reasoning in vision-language models (VLMs) face limitations, including the risk of test data contamination from textbook-based benchmarks, overemphasis on final answers over reasoning processes, and insufficient diagnostic granularity. To address these issues, we present GeoBench, a hierarchical benchmark featuring four reasoning levels in geometric problem-solving: Visual Perception, Goal-Oriented Planning, Rigorous Theorem Application, and Self-Reflective Backtracking. Through six formally verified tasks generated via TrustGeoGen, we systematically assess capabilities ranging from attribute extraction to logical error correction. Experiments reveal that while reasoning models like OpenAI-o3 outperform general MLLMs, performance declines significantly with increasing task complexity. Key findings demonstrate that sub-goal decomposition and irrelevant premise filtering critically influence final problem-solving accuracy, whereas Chain-of-Thought prompting unexpectedly degrades performance in some tasks. These findings establish GeoBench as a comprehensive benchmark while offering actionable guidelines for developing geometric problem-solving systems. Our benchmark and code are released at https://anonymous.4open.science/r/GeoBench-4BF4.
BibTeX
@inproceedings{
feng2026geobench,
title={GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation},
author={Yuan Feng and Yue Yang and Xiaohan He and Jiatong Zhao and Jianlong Chen and Daocheng Fu and Qi Liu and Renqiu Xia and Bo Zhang and Junchi Yan},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=pcmgEGVaZH}
}