Universality of Neural Network Field Theory

Abstract

We prove that any quantum field theory, or more generally any probability distribution over tempered distributions in ${\mathbb{R}}^d$, admits a neural network description with a countable infinity of parameters. As an example, we realize the $2d$ Liouville theory as a neural network and numerically compute the three-point function of vertex operators, finding agreement with the DOZZ formula.

arXiv comment6 pages, plus supplemental material (appendices)