Title: The representation theory of equivariant neural networks and graph neural nets
Abstract: Incorporating symmetries is an important theme in several branches of deep learning. However, there are a few domains where it is truly critical, including learning the behavior of physical systems and learning from sets/ and graphs. I will give an overview of some of the developments of the last few years in the area of equivariant neural networks, emphasizing the connections to group representation theory. In the second part of the talk I will talk about how this theory relates to graph neural networks, and how it might be used to generalize the popular message passing networks to more expressive architectures. The work presented in the talk has been done in collaboration with multiple researchers, including (in no particular order) Shubhendu Trivedi, Erik Thiede, Wenda Zhou, Brandon Anderson, Hy Truong Son and Horace Pan.