Deep Learning the Hyperbolic Volume of a Knot

Abstract

Abstract 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, Vol ( K ) . A less studied question is whether Vol ( K ) can be recovered directly from the original Jones polynomial ( N = 2 ). In this report we use a deep neural network to approximate 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.