Conformal Fields from Neural Networks

Fuente: arXiv
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Main Authors: Halverson, James, Naskar, Joydeep, Tian, Jiahua
Format: Preprint
Published: 2024
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author Halverson, James
Naskar, Joydeep
Tian, Jiahua
author_facet Halverson, James
Naskar, Joydeep
Tian, Jiahua
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_12222
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Conformal Fields from Neural Networks
Halverson, James
Naskar, Joydeep
Tian, Jiahua
High Energy Physics - Theory
Machine Learning
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.
title Conformal Fields from Neural Networks
topic High Energy Physics - Theory
Machine Learning
url https://arxiv.org/abs/2409.12222