What question did this study set out to answer?

To develop a formalism for constructing conformally invariant defects within neural network field theories.

May 14, 2026Journal of High Energy Physics0 citationsOpen Access

Conformal defects in neural network field theories

PCPietro CapuozzoNIHR Southampton Biomedical Research Centre BRBrandon RobinsonUniversity of Amsterdam BSBenjamin SuzzoniNIHR Southampton Biomedical Research Centre

Key Points

To develop a formalism for constructing conformally invariant defects within neural network field theories.
Defined symmetry-breaking patterns in network architecture and parameter priors.
Applied the formalism through two scalar field toy models.
Introduced the Neural Product Expansion (NPE) for analyzing defect spectra.
Successfully demonstrated the construction of conformal defects in neural networks.
Utilized the NPE framework to systematically analyze ambient correlation functions.
Decomposed correlation functions into defect spectra using the adaptation of defect OPE.

Abstract

A bstract 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 NN-FTs by specifying the symmetry-breaking patterns in the network architecture and parameter priors. We demonstrate this formalism through two scalar field toy models. To analyze these theories, we introduce the Neural Product Expansion (NPE); this framework adapts the defect OPE to the probabilistic nature of neural networks, providing a systematic method for decomposing ambient correlation functions into their defect spectra.

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