aiqbench analysis
This study applies reinforcement learning and Bayesian optimization to solve geometric topology problems, specifically calculating the slice genus and unknotting number for links where traditional algorithms fail. By training agents to find new unknotting trajectories, the research demonstrates a concrete intersection of machine learning techniques with non-computable mathematical invariants.
Computations of the slice genus and the unknotting number of links via machine learning
arXiv:2610.10206v1 Announce Type: cross 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.
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.
Geometric Topology (math.GT); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2610.10206 [math.GT]
(or arXiv:2610.10206v1 [math.GT] for this version)
https://doi.org/10.48550/arXiv.2610.10206 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 200 words
