# Preserving gauge invariance in neural networks

arXiv: https://arxiv.org/abs/2112.11239 · HTML: https://mlsanity.com/paper/2112.11239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Builds on (most cited first, 7 of 7)

- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [A high-bias, low-variance introduction to Machine Learning for physicists](https://mlsanity.com/paper/1803.08823/) (2018)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window](https://mlsanity.com/paper/2009.10971/) (2020)

## Built on by (most cited first, 1 of 1)

- [Deep learning lattice gauge theories](https://mlsanity.com/paper/2405.14830/) (2024)

## Abstract (arXiv)

In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the architecture and show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice. We compare the performance of L-CNNs and non-equivariant networks using a non-linear regression problem and demonstrate how gauge invariance is broken for non-equivariant models.