Covariance in Physics and Convolutional Neural Networks

In this proceeding we give an overview of the idea of covariance (or equivariance) featured in the recent development of convolutional neural networks (CNNs). We study the similarities and differences between the use of covariance in theoretical physics and in the CNN context. Additionally, we demonstrate that the simple assumption of covariance, together with the required properties of locality, linearity and weight sharing, is sufficient to uniquely determine the form of the convolution.