Using and Abusing Equivariance
Tom Edixhoven Attila Lengyel Jan van Gemert
In this paper we show how Group Equivariant Convolutional Neural Networks use
subsampling to learn to break equivariance to their symmetries. We focus on 2D
rotations and reflections and investigate the impact of broken equivariance on
network performance. We show that a change in the input dimension of a network
as small as a single pixel can be enough for commonly used architectures to
become approximately equivariant, rather than exactly. We investigate the
impact of networks not being exactly equivariant and find that approximately
equivariant networks generalise significantly worse to unseen symmetries
compared to their exactly equivariant counterparts. However, when the
symmetries in the training data are not identical to the symmetries of the
network, we find that approximately equivariant networks are able to relax
their own equivariant constraints, causing them to match or outperform exactly
equivariant networks on common benchmark datasets.