CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves

원문 초록

We introduce CurveBench, a benchmark for visual topological reasoning. Given an image of disjoint closed curves, a model must recover the tree of adjacent regions rooted at the exterior. The benchmark contains 756 hand-drawn images, ranging from simple configurations to maze-like and densely packed arrangements. Each image has a manually verified reference tree. We evaluate predictions by exact tree matching with the exterior root fixed. Gemini 3.1 Pro, the strongest model in our evaluation, achieves 71.1% exact-match accuracy on CurveBench-Easy and 28.7% on CurveBench-Hard. A Qwen3-VL-8B checkpoint trained using reinforcement learning with verifiable rewards reaches 31.7% on Easy, compared with 21.7% for its Thinking base model at a 16,384-token generation budget. The same comparison yields a gain of 1.1 percentage points on Hard.