EQUIVARIANT AND COORDINATE INDEPENDENT CONVOLUTIONAL NETWORKS: A GAUGE FIELD THEORY OF NEURAL NETWORKS

What is the appropriate geometric structure for neural networks that process spatial signals on Euclidean spaces or more general manifolds? This question takes us on a journey which leads to a gauge field theory of convolutional networks.

Feature vector fields: The spatial signals we are interested in are fields of feature vectors. Feature fields allow to describe data like images, audio, videos, point clouds, or tensor fields, such as fluid flows and electromagnetic …