Scholarlink

<p>We use the embedding formalism to construct conformal fields in <i>D</i> dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in (<i>D</i> + 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Conformal fields from neural networks

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月3日

查看全文
  • James Halverson,
  • Joydeep Naskar,
  • Jiahua Tian

摘要

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.