Conformal Defects in Neural Network Field Theories

TL;DR

This paper introduces a formalism for constructing conformally invariant defects within Neural Network Field Theories, demonstrated through toy models and an interpretation of defect operator product expansion.

Contribution

It presents a novel formalism for conformally invariant defects in NN-FTs, expanding the theoretical framework of neural network-based field theories.

Findings

Developed a formalism for conformally invariant defects in NN-FTs

Demonstrated the formalism in two toy scalar field models

Provided an NN interpretation of defect OPE expansion

Abstract

Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters. In this work, we present a formalism for the construction of conformally invariant defects in these NN-FTs. We demonstrate this new formalism in two toy models of NN scalar field theories. We develop an NN interpretation of an expansion akin to the defect OPE in two-point correlation functions in these models.