an:07166091
Zbl 1430.57001
Jejjala, Vishnu; Kar, Arjun; Parrikar, Onkar
Deep learning the hyperbolic volume of a knot
EN
Phys. Lett., B 799, Article ID 135033, 7 p. (2019).
00446333
2019
j
57-08 57K14 68T07
machine learning; neural network; topological field theory; knot theory
Summary: An important conjecture in knot theory relates the large-\(N\), double scaling limit of the colored Jones polynomial \(J_{K, N}(q)\) of a knot \(K\) to the hyperbolic volume of the knot complement, \(\operatorname{Vol}(K)\). A less studied question is whether \(\operatorname{Vol}(K)\) can be recovered directly from the original Jones polynomial \((N = 2)\). In this report, we use a deep neural network to approximate \(\operatorname{Vol}(K)\) from the Jones polynomial. Our network is robust and correctly predicts the volume with 97.6\% accuracy when training on 10\% of the data. This points to the existence of a more direct connection between the hyperbolic volume and the Jones polynomial.