Viability of perturbative expansion for quantum field theories on neurons

TL;DR

This study investigates the use of neural network architectures for perturbative calculations in quantum field theories, focusing on their convergence properties and potential modifications for improved accuracy.

Contribution

It evaluates the viability of NN-based approaches for finite neuron numbers in QFT perturbation theory and proposes architectural modifications to enhance convergence.

Findings

Renormalized $O(1/N)$ corrections show weak convergence due to UV cut-off sensitivity.

Proposed architecture modifications improve the convergence of perturbative series.

Identified parameter constraints and scaling laws for accurate QFT results.

Abstract

Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number $N$ using scalar $\phi^4$ theory in $d$ Euclidean dimensions as an example. We find that the renormalized $O(1/N)$ corrections to two- and four-point correlators yield perturbative series which are sensitive to the ultraviolet cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.