In this talk I present our progress on lattice gauge equivariant convolutional neural networks (L-CNNs). These new types of neural networks are a variant of convolutional neural networks (CNNs) which exactly preserve lattice gauge symmetry. By explicitly accounting for parallel transport in convolutions and allowing for bilinear operations inside the network, we show that L-CNNs can be used to approximate any gauge covariant function on the lattice. We demonstrate that our L-CNN models vastly outperform traditional CNNs in regression tasks such as computing Wilson loops from lattice gauge field configurations. In addition, we show that our L-CNN models can be trained on data from small lattices while still performing well on larger lattices.
 "Lattice gauge equivariant convolutional neural networks", M. Favoni, A. Ipp, D. I. Müller, D. Schuh, https://arxiv.org/abs/2012.12901