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| Autori principali: | , , , |
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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.12488 |
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| _version_ | 1866917487212232704 |
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| author | Ferko, Christian Frank, Samuel Halverson, James Jejjala, Vishnu |
| author_facet | Ferko, Christian Frank, Samuel Halverson, James Jejjala, Vishnu |
| contents | 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 $4d$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Anomalies in Neural Network Field Theory Ferko, Christian Frank, Samuel Halverson, James Jejjala, Vishnu High Energy Physics - Theory 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 $4d$ 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. |
| title | Anomalies in Neural Network Field Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.12488 |