  Convolutional neural networks revolutionized computer vision and natrual
language processing. Their efficiency, as compared to fully connected neural
networks, has its origin in the architecture, where convolutions reflect the
translation invariance in space and time in pattern or speech recognition
tasks. Recently, Cohen and Welling have put this in the broader perspective of
invariance under symmetry groups, which leads to the concept of group
equivaiant neural networks and more generally steerable neural networks. In
this article, we review the architecture of such networks including equivariant
layers and filter banks, activation with capsules and group pooling. We apply
this formalism to the symmetric group, for which we work out a number of
details on representations and capsules that are not found in the literature.
