Anomalies in neural network field theory
- 1Northeastern University
- 2The NSF Institute for Artificial Intelligence and Fundamental Interactions (IAIFI)
- 3University of the Witwatersrand
Abstract
A bstract : Neural network field theory (NN-FT) formulates field theory in terms of a network architecture and a density on its parameters. We derive Schwinger–Dyson equations and Ward identities in NN-FT and utilize them to study anomalies. The equations depend on a conserved parameter space current that characterizes symmetries and how they break. It is relevant even in non-local NN-FTs, but can recover local currents in the case of a local Lagrangian by an appropriate fiber-wise average. In machine learning, this formalism is applied to feedforward networks and the attention mechanism. In physics, we use this machinery to study U(1) symmetry for a complex scalar, the scale anomaly in 4 d massless ϕ ⁴ theory, the Weyl anomaly for the bosonic string (including a new computation of the critical dimension), and examples involving discrete topological data, such as winding numbers and T-duality. Since the results are obtained in network parameter space rather than the standard field space, they represent a new way to understand symmetries in quantum field theories.
Related
- What Neural Network Field Theory Can and Cannot Realise on a Computer
- Constructive Neural Network Field Theory: ϕ24 in Finite Volume
- A Pedagogical Introduction to Anomalies in Quantum Field Theory
- Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials
- Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Kohn--Sham method
BibTeX
@article{ferko2026anomalies,
title = {{Anomalies in neural network field theory}},
author = {Christian Ferko and Samuel Frank and James Halverson and Vishnu Jejjala},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)143},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)143},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Anomalies in neural network field theory
AU - Christian Ferko
AU - Samuel Frank
AU - James Halverson
AU - Vishnu Jejjala
PY - 2026
DA - 2026/10/14
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)143
UR - https://link.springer.com/article/10.1007/JHEP10(2026)143
AB - A bstract : Neural network field theory (NN-FT) formulates field theory in terms of a network architecture and a density on its parameters. We derive Schwinger–Dyson equations and Ward identities in NN-FT and utilize them to study anomalies. The equations depend on a conserved parameter space current that characterizes symmetries and how they break. It is relevant even in non-local NN-FTs, but can recover local currents in the case of a local Lagrangian by an appropriate fiber-wise average. In machine learning, this formalism is applied to feedforward networks and the attention mechanism. In physics, we use this machinery to study U(1) symmetry for a complex scalar, the scale anomaly in 4 d massless ϕ ⁴ theory, the Weyl anomaly for the bosonic string (including a new computation of the critical dimension), and examples involving discrete topological data, such as winding numbers and T-duality. Since the results are obtained in network parameter space rather than the standard field space, they represent a new way to understand symmetries in quantum field theories.
SN - 1029-8479
ER -