arXiv：cs.LG· Yutong Dai, Oliver Hayman, Andr\'as Juh\'asz, Ludovico Morellato·· 4 小时前AI 评分32
用机器学习计算链的切片亏格与解结数
Computations of the slice genus and the unknotting number of links via machine learning
AI 导读
研究用强化学习与贝叶斯优化，对切片亏格、链的解结数以及代数分裂链的强切片亏格给出新的上界，并结合已知不变量计算下界，从而在许多情形下得到新的精确值。解结智能体还能复现 Brittenham 和 Hermiller 给出的多个反例中解结数的非可加性，部分情形下找到了新的解结路径。
正文
Abstract:Links are disjoint unions of circles smoothly embedded in $S^3$. We use reinforcement learning and Bayesian optimisation to obtain new upper bounds on several link invariants that are not known to be algorithmically computable: the slice genus and the unknotting number for links, and the strong slice genus for algebraically split links. We also compute lower bounds using known invariants. Combining the upper and lower bounds, we obtain new exact values in many cases. Our unknotting agents can reproduce the non-additivity of the unknotting number for several counterexamples due to Brittenham and Hermiller, in some cases finding new unknotting trajectories.
| Comments: | 72 pages, 34 figures |
| Subjects: | Geometric Topology (math.GT); Machine Learning (cs.LG); Machine Learning (stat.ML) |
| MSC classes: | 57K10, 68T07 (Primary) 57K14, 57K18 (Secondary) |
| ACM classes: | I.2.1; I.2.6 |
| Cite as: | arXiv:2610.10206 [math.GT] |
| (or arXiv:2610.10206v1 [math.GT] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10206 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Andras Juhász [view email]
[v1]
Wed, 7 Oct 2026 15:04:04 UTC (1,136 KB)
来源：arXiv：cs.LG · arxiv.org