Preserving gauge invariance in neural networks
This work addresses the challenge of ensuring gauge invariance in neural networks for physics simulations, which is crucial for accurate modeling in lattice gauge theory.
The paper tackled the problem of preserving gauge symmetry in neural networks for lattice gauge theory simulations by introducing lattice gauge equivariant convolutional neural networks (L-CNNs), and demonstrated that L-CNNs maintain gauge invariance while non-equivariant models break it in a non-linear regression task.
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.