Lattice gauge equivariant convolutional neural networks
This work addresses the problem of preserving gauge equivariance in neural networks for lattice gauge theory, which is significant for physicists working on these theoretical problems.
This paper proposes Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) to address machine learning problems in lattice gauge theory. The L-CNNs are shown to learn and generalize gauge invariant quantities that traditional CNNs fail to identify.
We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.