Illuminating new and known relations between knot invariants
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915686942507008 |
|---|---|
| author | Craven, Jessica Hughes, Mark Jejjala, Vishnu Kar, Arjun |
| author_facet | Craven, Jessica Hughes, Mark Jejjala, Vishnu Kar, Arjun |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01404 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Illuminating new and known relations between knot invariants Craven, Jessica Hughes, Mark Jejjala, Vishnu Kar, Arjun Geometric Topology High Energy Physics - Theory 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. |
| title | Illuminating new and known relations between knot invariants |
| topic | Geometric Topology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2211.01404 |