Using equivariant neural networks as maps of gauge field configurations

Abstract

Lattice gauge equivariant convolutional neural networks (L-CNNs) are neural networks consisting of layers that respect gauge symmetry. They can be used to predict physical observables, but also to modify gauge field configurations. The approach proposed here is to treat a gradient flow equation as a neural ordinary differential equation parametrized by L-CNNs. Training these types of networks with standard backpropagation usually requires to store the intermediate states of the flow time evolution, which can easily lead to memory saturation issues. A solution to this problem is offered by the adjoint sensitivity method. We present our derivation and test our approach on toy models.