  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.
