Illuminating new and known relations between knot invariants
We automate the process of machine learning correlations between knot invariants. For nearly 200 000 distinct sets of input knot invariants together with an output invariant, we attempt to learn the output invariant by training a neural network on the input invariants. Correlation between invariants...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/ad95d9 |
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| author | Jessica Craven Mark Hughes Vishnu Jejjala Arjun Kar |
| author_facet | Jessica Craven Mark Hughes Vishnu Jejjala Arjun Kar |
| author_sort | Jessica Craven |
| collection | DOAJ |
| description | We automate the process of machine learning correlations between knot invariants. For nearly 200 000 distinct sets of input knot invariants together with an output invariant, we attempt to learn the output invariant by training a neural network on the input invariants. Correlation between invariants is measured by the accuracy of the neural network prediction, and bipartite or tripartite correlations are sequentially filtered from the input invariant sets so that experiments with larger input sets are checking for true multipartite correlation. We rediscover several known relationships between polynomial, homological, and hyperbolic knot invariants, while also finding novel correlations which are not explained by known results in knot theory. These unexplained correlations strengthen previous observations concerning links between Khovanov and knot Floer homology. Our results also point to a new connection between quantum algebraic and hyperbolic invariants, similar to the generalized volume conjecture. |
| format | Article |
| id | doaj-art-76240b4834a3428e9beb31b7bbac974f |
| institution | OA Journals |
| issn | 2632-2153 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-76240b4834a3428e9beb31b7bbac974f2025-08-20T01:59:21ZengIOP PublishingMachine Learning: Science and Technology2632-21532024-01-015404506110.1088/2632-2153/ad95d9Illuminating new and known relations between knot invariantsJessica Craven0Mark Hughes1https://orcid.org/0000-0001-6305-2949Vishnu Jejjala2https://orcid.org/0000-0003-2603-6717Arjun Kar3https://orcid.org/0000-0003-1943-4346Division of Physics, Mathematics, and Astronomy (PMA), California Institute of Technology , Pasadena, CA 91125, United States of AmericaDepartment of Mathematics, Brigham Young University , 275 TMCB, Provo, UT 84602, United States of America; Max Planck Institute for Mathematics , Vivatsgasse 7, 53111 Bonn, GermanyMandelstam Institute for Theoretical Physics, School of Physics, NITheCS, and CoE-MaSS, University of the Witwatersrand , 1 Jan Smuts Avenue, Johannesburg WITS 2050, South AfricaDepartment of Physics and Astronomy, University of British Columbia , 6224 Agricultural Road, Vancouver, BC V6T 1Z1, CanadaWe automate the process of machine learning correlations between knot invariants. For nearly 200 000 distinct sets of input knot invariants together with an output invariant, we attempt to learn the output invariant by training a neural network on the input invariants. Correlation between invariants is measured by the accuracy of the neural network prediction, and bipartite or tripartite correlations are sequentially filtered from the input invariant sets so that experiments with larger input sets are checking for true multipartite correlation. We rediscover several known relationships between polynomial, homological, and hyperbolic knot invariants, while also finding novel correlations which are not explained by known results in knot theory. These unexplained correlations strengthen previous observations concerning links between Khovanov and knot Floer homology. Our results also point to a new connection between quantum algebraic and hyperbolic invariants, similar to the generalized volume conjecture.https://doi.org/10.1088/2632-2153/ad95d9knotsknot invariantsmachine learningneural networks |
| spellingShingle | Jessica Craven Mark Hughes Vishnu Jejjala Arjun Kar Illuminating new and known relations between knot invariants Machine Learning: Science and Technology knots knot invariants machine learning neural networks |
| title | Illuminating new and known relations between knot invariants |
| title_full | Illuminating new and known relations between knot invariants |
| title_fullStr | Illuminating new and known relations between knot invariants |
| title_full_unstemmed | Illuminating new and known relations between knot invariants |
| title_short | Illuminating new and known relations between knot invariants |
| title_sort | illuminating new and known relations between knot invariants |
| topic | knots knot invariants machine learning neural networks |
| url | https://doi.org/10.1088/2632-2153/ad95d9 |
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