Covariance in Physics and Convolutional Neural Networks

In his words, the general principle of covariance states that "The general laws of nature are In this proceeding we give an overview of the to be expressed by equations which hold good for all systems idea of covariance (or equivariance) featured in of coordinates, that is, are covariant with respect to the recent development of convolutional neural any substitutions whatever (generally covariant)" (Einstein, networks (CNNs). We study the similarities and 1916). The rest is history: the incorporation of the mathematics differences between the use of covariance in theoretical of Riemannian geometry in order to achieve general physics and in the CNN context. Additionally, covariance and the formulation of the general relativity we demonstrate that the simple assumption (GR) theory of gravity. It is important to note that the seemingly of covariance, together with the required properties innocent assumption of general covariance is in fact of locality, linearity and weight sharing, is so powerful that it determines GR as the unique theory of sufficient to uniquely determine the form of the gravity compatible with this principle, and the equivalence convolution.