Before revision:  The theory enables a systematic classification of all existing G-CNNs in terms of their group of symmetry , base space, and field type (e. g. scalar, vector, or tensor field, etc.). In addition to this classification, we use Mackey theory to show that convolutions with equivariant kernels are the most general class of equivariant maps between such fields, thus establishing G-CNNs as a universal class of equivariant networks.
After revision:  The theory enables a systematic classification of all existing G-CNNs in terms of their group of symmetry , base space, and field type . We also consider a fundamental question: what is the most general class of equivariant maps between such fields, thus establishing G-CNNs as a universal class of equivariant networks.