Deep learning the hyperbolic volume of a knot

An important conjecture in knot theory relates the large-N, double scaling limit of the colored Jones polynomial JK,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.