Machine learning applications in string theory

Abstract

We demonstrate the effectiveness of machine learning techniques as research tools in formal theory. In knot theory (and consequently the related quantum field theories, such as Chern–Simons theory), we use artificial neural networks as tools to identify relationships in large datasets. Specifically, we are able to predict the slice genus and s-invariant of knots from the Jones polynomial. Further, we show how inter- pretable machine learning techniques can be used to derive new analytic formulae from machine learning results. These interpretation techniques allow us to reverse engineer a neural network to predict the hyperbolic volume from evaluations of the Jones polynomial. We also demonstrate how Restricted Boltzmann Machines can be used to study computationally difficult problems, such as computing out of time ordered correlators of the SYK model. We discuss applications of this technique to numerically mapping out the phase space of chaos.