Abstract:

Convolution is a natural operation combining two integrable functions on Euclidean space. This operation motivates the definition of “convolutional neural networks”. On manifolds, there is no natural convolution operation for functions. But there is if we restrict to functions that are invariant under the holonomy group, or if we restrict functions to a graph embedded in the manifold. This motivates the definition of “graph convolutional networks” and “gauge equivariant convolutional networks”. I will explain the convolution operators, and if time permits will show that they agree in a simple setting and state the open problem of proving that they agree in general.