Conformal fields from neural networks

We use the embedding formalism to construct conformal fields in D dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in (D + 2) dimensions to the projective null cone. Conformal correlators may be computed using the parameter space description of the neural network. Exact four-point correlators are computed in a number of examples, and we perform a 4D conformal block decomposition that elucidates the spectrum. In a non-unitary example the decomposition precisely matches OPE coefficients for the self-correlator, but not for the mixed correlator. In others, the analysis is facilitated by recent approaches to Feynman integrals. Generalized free CFTs are constructed using the infinite-width Gaussian process limit of the neural network, enabling a realization of the free boson. The extension to deep networks constructs conformal fields at each subsequent layer, with recursion relations relating their conformal dimensions and four-point functions. Numerical approaches are discussed.