# Conformal Fields from Neural Networks

arXiv: https://arxiv.org/abs/2409.12222 · HTML: https://mlsanity.com/paper/2409.12222/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 63 references that are in the map.
- First posted on arXiv 18 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators](https://mlsanity.com/paper/2106.00694/) (2021)
- [Building Quantum Field Theories Out of Neurons](https://mlsanity.com/paper/2112.04527/) (2021)
- [Neural Network Field Theories: Non-Gaussianity, Actions, and Locality](https://mlsanity.com/paper/2307.03223/) (2023)
- [TASI Lectures on Physics for Machine Learning](https://mlsanity.com/paper/2408.00082/) (2024)

## Built on by (most cited first, 11 of 11)

- [Fermions and Supersymmetry in Neural Network Field Theories](https://mlsanity.com/paper/2511.16741/) (2025)
- [Gauge-covariant stochastic neural fields: Stability and finite-width effects](https://mlsanity.com/paper/2508.18948/) (2025)
- [Conformal Defects in Neural Network Field Theories](https://mlsanity.com/paper/2512.07946/) (2025)
- [Virasoro Symmetry in Neural Network Field Theories](https://mlsanity.com/paper/2512.24420/) (2025)
- [AdS-GNN -- a Conformally Equivariant Graph Neural Network](https://mlsanity.com/paper/2505.12880/) (2025)
- [Viability of perturbative expansion for quantum field theories on neurons](https://mlsanity.com/paper/2508.03810/) (2025)
- [Topological Effects in Neural Network Field Theory](https://mlsanity.com/paper/2604.02313/) (2026)
- [Spinning Conformal Correlators from Neural Networks](https://mlsanity.com/paper/2608.15001/) (2026)
- [Bulk-boundary decomposition of neural networks](https://mlsanity.com/paper/2511.02003/) (2025)
- [Deep neural networks as lattice gauge theories](https://mlsanity.com/paper/2608.19331/) (2026)
- [What Neural Network Field Theory Can and Cannot Realise on a Computer](https://mlsanity.com/paper/2608.21523/) (2026)

## Abstract (arXiv)

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.