Gauge equivariant convolutional neural networks

Abstract

In this thesis we present a review of the current theory of group and gauge equivariant convolutional neural networks on homogeneous spaces and general smooth manifolds, with focus on the latter, formulated from a mathematical viewpoint. We also provide a new interpretation of layers in neural networks as maps between associated bundles. Furthermore we discuss the implementation of simple convolutional neural networks invariant under 90 rotations and reflections, build such networks, and test them to show the effect of the invariant construction. This testing shows that the addition of the group invariant structure allows the network to efficiently classify transformed data while only training on untransformed data.