# Applications of Lattice Gauge Equivariant Neural Networks

arXiv: https://arxiv.org/abs/2212.00832 · HTML: https://mlsanity.com/paper/2212.00832/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 6 references that are in the map.
- First posted on arXiv 1 Dec 2022.

## Builds on (most cited first, 4 of 4)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)

## Built on by (most cited first, 2 of 2)

- [Deep learning lattice gauge theories](https://mlsanity.com/paper/2405.14830/) (2024)
- [Learnable cut flow for high energy physics](https://mlsanity.com/paper/2503.22498/) (2025)

## Abstract (arXiv)

The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge symmetries, which are incorporated into the network layers of our recently proposed Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs). L-CNNs can generalize better to differently sized lattices than traditional neural networks and are by construction equivariant under lattice gauge transformations. In these proceedings, we present our progress on possible applications of L-CNNs to Wilson flow or continuous normalizing flow. Our methods are based on neural ordinary differential equations which allow us to modify link configurations in a gauge equivariant manner. For simplicity, we focus on simple toy models to test these ideas in practice.