Before revision:  A wide variety of equivariant layers has been proposed for signals on 2D and 3D Euclidean space , graphs, and the sphere , and it has become difficult to see how all of these methods are related, and how they may be generalized. In this paper, we present a fairly general theory of equivariant convolutional networks . Convolutional feature spaces are described as fields over a homogeneous base space, such as the plane \mathbb{R .
After revision:  A wide variety of equivariant layers has been proposed for signals on 2D and 3D Euclidean space , graphs, and the sphere . Feature maps in these networks represent fields on a homogeneous base space, such as the plane \mathbb{R .