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 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.

For a steel company it is advantageous to be able to easily track steel through the production process. At Tata Steel this is currently done with the Material Tracking Table. However, generating this table takes months. Therefore a new system had to be developed. This paper describes the building of such a new system, which generates this Material Tracking Table in less than 1 hour, as well as the related systems concerning the acquisition of the input data and the visualisation of the resulting output data.