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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2025-01-01
|
| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/ade362 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849688048656187392 |
|---|---|
| author | Sergei Gukov James Halverson Ciprian Manolescu Fabian Ruehle |
| author_facet | Sergei Gukov James Halverson Ciprian Manolescu Fabian Ruehle |
| author_sort | Sergei Gukov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e42d8b44641f434fb39b82eda4d27ce9 |
| institution | DOAJ |
| issn | 2632-2153 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-e42d8b44641f434fb39b82eda4d27ce92025-08-20T03:22:09ZengIOP PublishingMachine Learning: Science and Technology2632-21532025-01-016202506510.1088/2632-2153/ade362Searching for ribbons with machine learningSergei Gukov0James Halverson1https://orcid.org/0000-0003-0535-2622Ciprian Manolescu2https://orcid.org/0000-0003-0600-8751Fabian Ruehle3https://orcid.org/0000-0002-8409-9823Dublin Institute for Advanced Studies , 10 Burlington Rd, Dublin, Ireland; California Institute of Technology , Pasadena, CA 91125, United States of AmericaDepartment of Physics, Northeastern University , 360 Huntington Avenue, Boston, MA 02115, United States of America; The NSF AI Institute for Artificial Intelligence and Fundamental Interactions , Boston, MA, United States of AmericaDepartment of Mathematics, Stanford University , 450 Jane Stanford Way, Building 380, Stanford, CA 94305-2125, United States of AmericaThe NSF AI Institute for Artificial Intelligence and Fundamental Interactions , Boston, MA, United States of America; Department of Physics and Department Mathematics, Northeastern University , 360 Huntington Avenue, Boston, MA 02115, United States of AmericaWe 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.https://doi.org/10.1088/2632-2153/ade362reinforcement learningBayesian optimizationknot theorylow-dimensional topology |
| spellingShingle | Sergei Gukov James Halverson Ciprian Manolescu Fabian Ruehle Searching for ribbons with machine learning Machine Learning: Science and Technology reinforcement learning Bayesian optimization knot theory low-dimensional topology |
| title | Searching for ribbons with machine learning |
| title_full | Searching for ribbons with machine learning |
| title_fullStr | Searching for ribbons with machine learning |
| title_full_unstemmed | Searching for ribbons with machine learning |
| title_short | Searching for ribbons with machine learning |
| title_sort | searching for ribbons with machine learning |
| topic | reinforcement learning Bayesian optimization knot theory low-dimensional topology |
| url | https://doi.org/10.1088/2632-2153/ade362 |
| work_keys_str_mv | AT sergeigukov searchingforribbonswithmachinelearning AT jameshalverson searchingforribbonswithmachinelearning AT ciprianmanolescu searchingforribbonswithmachinelearning AT fabianruehle searchingforribbonswithmachinelearning |