Conformal Fields from Neural Networks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918154133831680 |
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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 |