GeoBench Overview: Verified Geometry Reasoning Tasks

Paper context

Paper title: GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation 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. Passages referencing this figure: Figure 1: Overview of GeoBench : (1) Generation of formally verified geometry problems with images, problems and reasoning graphs via TrustGeoGen ( trustgeogen2025 ) , followed by (2) systematic construction of hierarchical evaluation tasks through four reasoning capability levels. As illustrated in Fig. 1 , the correct path 𝒫 \mathcal{P} (the goal-oriented reasoning path marked in Fig.