Using and Abusing Equivariance: Investigating Differences between Exact and Approximate Equivariance in Computer Vision

In this work we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on the 2D roto-translation group and investigate the impact of broken equivariance on network performance. We show that changing the input dimension of a network by as little as a single pixel can...