Before revision:  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:  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, and layers are equivariant maps between spaces of fields .