Journal Article

Neural networks and quantum field theory

Halverson, James, Maiti, Anindita, Stoner, Keegan

2021

Overview

We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes (GPs), the analog of non-interacting field theories. Moving away from the asymptotic limit yields a non-Gaussian process (NGP) and corresponds to turning on particle interactions, allowing for the computation of correlation functions of neural network outputs with Feynman diagrams. Minimal NGP likelihoods are determined by the most relevant non-Gaussian terms, according to the flow in their coefficients induced by the Wilsonian renormalization group. This yields a direct connection between overparameterization and simplicity of neural network likelihoods. Whether the coefficients are constants or functions may be understood in terms of GP limit symmetries, as expected from ’t Hooft’s technical naturalness. General theoretical calculations are matched to neural network experiments in the simplest class of models allowing the correspondence. Our formalism is valid for any of the many architectures that becomes a GP in an asymptotic limit, a property preserved under certain types of training.

• Publisher: IOP Publishing
• Subject: Asymptotic properties / Feynman diagrams / Field theory / finite width NN / Gaussian process / Gaussian processes / infinite width NNGP / Neural networks / Particle interactions / Quantum field theory / Quantum theory / Wilsonian RG flow