Conformal defects in neural network field theories

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.