Seminar Geometry, Algebra and Physics in Deep Neural Networks (GAPinDNNs)

Abstract: Equivariance imposes symmetry constraints on the connectivity of neural networks. This talk investigates the case of equivariant networks for fields of feature vectors on Euclidean spaces or other Riemannian manifolds. Equivariance is shown to lead to requirements for 1) spatial (convolutional) weight sharing, and 2) symmetry constraints on the shared weights themselves. We investigate the symmetry constraints imposed on convolution kernels and discuss how they can be solved and implemented. A gauge theoretic formulation of equivariant CNNs shows that these models are not only equivariant under global transformations, but under more general local gauge transformations as well.