Conformal Fields from Neural Networks
<|reference_start|>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 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.<|reference_end|>
@article{halverson2024conformal,
    title={Conformal Fields from Neural Networks},
    author={James Halverson, Joydeep Naskar, Jiahua Tian},
    journal={arXiv preprint arXiv:2409.12222},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12222},
    primaryClass={hep-th cs.LG}
}