{"ID":2823971,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24119","arxiv_id":"2512.24119","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.","short_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, o...","url_abs":"https://arxiv.org/abs/2512.24119","url_pdf":"https://arxiv.org/pdf/2512.24119v1","authors":"[\"Yuan Feng\",\"Yue Yang\",\"Xiaohan He\",\"Jiatong Zhao\",\"Jianlong Chen\",\"Zijun Chen\",\"Daocheng Fu\",\"Qi Liu\",\"Renqiu Xia\",\"Bo Zhang\",\"Junchi Yan\"]","published":"2025-12-30T09:56:37Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[\"Large Language Model\",\"Language Model\"]","has_code":false}