Searching for ribbons with machine learning

Searching for ribbons with machine learning

We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincaré conjecture; using our programs, we rule out many potential counterexamples...

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Bibliographic Details
Main Authors: Sergei Gukov, James Halverson, Ciprian Manolescu, Fabian Ruehle
Format: Article
Language:English
Published: IOP Publishing 2025-01-01
Series:Machine Learning: Science and Technology
Subjects:
reinforcement learning
Bayesian optimization
knot theory
low-dimensional topology
Online Access:https://doi.org/10.1088/2632-2153/ade362
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Summary:We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincaré conjecture; using our programs, we rule out many potential counterexamples to the conjecture. We also show that the programs are successful in detecting many ribbon knots in the range of up to 70 crossings.
ISSN:2632-2153

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