CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves
CurveBench is a new benchmark for evaluating visual topological reasoning in AI. It consists of 756 images of nested Jordan curves and requires models to reconstruct containment trees. Top models like Gemini 3.1 Pro achieve only 71.1% on easy and 19.1% on hard. Fine-tuning with RLVR improves small models significantly, but the task remains challenging.
[2605.14068] CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves
[Submitted on 13 May 2026]
Title:CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves
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Abstract:We introduce CurveBench, a benchmark for hierarchical topological reasoning from visual input. CurveBench consists of \textbf{756 images} of pairwise non-intersecting Jordan curves across easy, polygonal, topographic-inspired, maze-like, and dense counting configurations. Each image is annotated with a rooted tree encoding the containment relations between planar regions. We formulate the task as structured prediction: given an image, a model must recover the full rooted containment tree induced by the curves. Despite the visual simplicity of the task, the strongest evaluated model, Gemini 3.1 Pro, achieves only \textbf{71.1\%} tree-generation accuracy on CurveBench-Easy and \textbf{19.1\%} on CurveBench-Hard. We further demonstrate benchmark utility through RLVR-style fine-tuning of open-weight vision-language models. Our trained Qwen3-VL-8B model improves over \texttt{Qwen-3-VL-8B-Thinking} from \textbf{2.8\%} to \textbf{33.3\%} tree-generation accuracy on CurveBench-Easy, exceeding GPT-5.4 and Claude Opus 4.5 under our evaluation protocol. The remaining gap, especially on CurveBench-Hard, shows that exact topology-aware visual reasoning remains far from solved.
Subjects:
Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)
Cite as: arXiv:2605.14068 [cs.CV]
(or arXiv:2605.14068v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2605.14068
arXiv-issued DOI via DataCite (pending registration)
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From: Morteza Saghafian [view email] [v1] Wed, 13 May 2026 19:46:22 UTC (2,934 KB)
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