Spinning Conformal Correlators from Neural Networks

Manas Dogra; James Halverson; Joydeep Naskar

hep-thAug 15, 2026

Spinning Conformal Correlators from Neural Networks

Authors: Manas Dogra, James Halverson, Joydeep Naskar

Organizations: Department of Physics, Northeastern University, Boston, MA, 02115, USA · The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, MA, U.S.A. · Beijing Institute of Mathematical Sciences and Applications, Huaibei Town, Huairou District, Beijing 101408, China

Abstract

We construct spinning conformal fields from neural networks and the embedding formalism, computing their two-, three- and four-point functions in examples, building on scalar conformal field techniques introduced in \cite{Halverson:2024axc}. For a particular ensemble of i.i.d. neurons we recover the 4d Maxwell CFT in the infinite-width limit.

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What Neural Network Field Theory Can and Cannot Realise on a Computer

Thomas R. Harvey

The NSF AI Institute for Artificial Intelligence and Fundamental Interactions. Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

High-Energy Physics

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One aim of neural network field theory is to put a quantum or effective field theory on a computer, with the network ensemble itself as the theory. We ask how far that aim can be pushed for a function class regular enough to be computed with. Our main result is a no-go theorem with assumptions that hold for standard network architectures. We use it to separate four versions of neural network field theory, according to whether the defining object is the finite width ensemble or its infinite width limit, and whether the target we want to compute is a quantum or an effective field theory. Neither finite width interpretation is straightforwardly consistent. For finite width ensembles with finite variance at each point, the QFT interpretation fails reflection positivity, while the EFT interpretation establishes no scale separation by which the positivity violation can be placed outside its domain of validity. Of the two limit versions, one can be simulated in full and the other only in part, as only its smeared correlators are computable with a controlled error. As such, at the level of a controlled numerical computation, the QFT and EFT versions cannot be distinguished. One dimension escapes the obstruction, yet reflection positivity is shown to still fail there at every finite width for the cosine network. Two escapes from the theorem remain, giving up either finite variance at a point or exact rotation invariance, and we discuss both of these possibilities.

Abstract

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