The Gordian Knot for VLMs: Diagrammatic Knot Reasoning as a Hard Benchmark
A vision-language model can look at a knot diagram and report what it sees, yet fail to act on that structure. KnotBench pairs an 858,318-image corpus from 1,951 prime-knot prototypes (crossing numbers 3 to 19) with a protocol whose answers are checked against Regina's canonical knot signature. Its 14 tasks span four families, equivalence judgment, move prediction, identification, and cross-modal grounding; an image-versus-symbol split locates failures along the perception-operation gap. We score Claude Opus 4.7 and GPT-5, each with and without thinking, under a 64K output-token budget matched on both vendors. Across 56 (task, model) cases, 15 sit at or below a random baseline and 8 of 14...
| Authors | Hao Liu, Jicheng Liu |
|---|---|
| Primary category | cs.AI |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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