Symmetry-preserving neural networks in lattice field theories

Fuente: arXiv
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Autore principale: Favoni, Matteo
Natura: Preprint
Pubblicazione: 2025
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author Favoni, Matteo
author_facet Favoni, Matteo
contents This thesis deals with neural networks that respect symmetries and presents the advantages in applying them to lattice field theory problems. The concept of equivariance is explained, together with the reason why such a property is crucial for the network to preserve the desired symmetry. The benefits of choosing equivariant networks are first illustrated for translational symmetry on a complex scalar field toy model. The discussion is then extended to gauge theories, for which Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs) are specifically designed ad hoc. Regressions of physical observables such as Wilson loops are successfully solved by L-CNNs, whereas traditional architectures which are not gauge symmetric perform significantly worse. Finally, we introduce the technique of neural gradient flow, which is an ordinary differential equation solved by neural networks, and propose it as a method to generate lattice gauge configurations.
format Preprint
id arxiv_https___arxiv_org_abs_2506_12493
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Symmetry-preserving neural networks in lattice field theories
Favoni, Matteo
High Energy Physics - Lattice
Machine Learning
This thesis deals with neural networks that respect symmetries and presents the advantages in applying them to lattice field theory problems. The concept of equivariance is explained, together with the reason why such a property is crucial for the network to preserve the desired symmetry. The benefits of choosing equivariant networks are first illustrated for translational symmetry on a complex scalar field toy model. The discussion is then extended to gauge theories, for which Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs) are specifically designed ad hoc. Regressions of physical observables such as Wilson loops are successfully solved by L-CNNs, whereas traditional architectures which are not gauge symmetric perform significantly worse. Finally, we introduce the technique of neural gradient flow, which is an ordinary differential equation solved by neural networks, and propose it as a method to generate lattice gauge configurations.
title Symmetry-preserving neural networks in lattice field theories
topic High Energy Physics - Lattice
Machine Learning
url https://arxiv.org/abs/2506.12493