There is great interest in generalizing deep learning to more exotic types of data, such as graphs, chemical structures, volumetric images, omndirectional images, etc. In each case, the data has nontrivial structure and symmetries and the challenge is to find the right generalization of classical neural network layers like convolution to reflect this. It has become clear that in all of these cases and more, equivariance to symmetry transformations is the key principle that points us to an effective generalization.

New architectures inspired by this principle have already proved their effectiveness in multiple domains. However, some of the underlying ideas are still foreign to much of the community, partly because of the mathematics involved. The purpose of this tutorial is to bridge this gap by giving a very accessible introduction to this emerging area with many practical examples and details of how to implement equivariant architectures in existing deep learning frameworks.

Timetable: Part I (Taco Cohen) 0:00 - Introduction to equivariant networks 39:00 - Examples and applications 51:00 - Equivariant convolutions

Part II (Risi Kondor) 0:00 - Introduction 7:50 - Group Representations 27:35 - Designing equivariant Neurons 45:30 - Fourier theory 56:25 - Implementation