RL unknotter, hard unknots and unknotting number
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913070498971648 |
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| author | Dranowski, Anne Kabkov, Yura Tubbenhauer, Daniel |
| author_facet | Dranowski, Anne Kabkov, Yura Tubbenhauer, Daniel |
| contents | We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on ``very hard'' unknot diagrams and, using diagram inflation, on $4_1\#9_{10}$ where we recover the recently established and surprising upper bound of three for the unknotting number. In addition, we explain a self-improving workbook-driven extension of the pipeline that systematically improves unknotting number upper bounds on the list of prime knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07955 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | RL unknotter, hard unknots and unknotting number Dranowski, Anne Kabkov, Yura Tubbenhauer, Daniel Geometric Topology Machine Learning Primary: 57K10, 68T05, Secondary: 57K14, 90C59 We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on ``very hard'' unknot diagrams and, using diagram inflation, on $4_1\#9_{10}$ where we recover the recently established and surprising upper bound of three for the unknotting number. In addition, we explain a self-improving workbook-driven extension of the pipeline that systematically improves unknotting number upper bounds on the list of prime knots. |
| title | RL unknotter, hard unknots and unknotting number |
| topic | Geometric Topology Machine Learning Primary: 57K10, 68T05, Secondary: 57K14, 90C59 |
| url | https://arxiv.org/abs/2603.07955 |