Conformal Fields from Neural Networks

• URL: http://arxiv.org/abs/2409.12222v2
• Date: Sat, 04 Oct 2025 20:36:27 GMT
• Title: Conformal Fields from Neural Networks
• Authors: James Halverson, Joydeep Naskar, Jiahua Tian,
• Abstract summary: We use the embedding formalism to construct conformal fields in $D$ dimensions.<n>We perform a 4D conformal block decomposition that elucidates the spectrum.<n>The extension to deep networks constructs conformal fields at each subsequent layer.
• Score: 1.497481482212619
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 some examples 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.

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