\dm_csml_event_details UCL ELLIS

Equivariant and coordinate independent convolutional networks


Maurice Weiler


University of Amsterdam


Friday, 17 June 2022




Function Space, UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH



Event series

DeepMind/ELLIS CSML Seminar Series


The classical convolutional network architecture can be derived solely from the requirement for translational equivariance. Steerable CNNs generalize this idea to affine symmetry groups, resulting in network architectures that are equivariant under additional symmetries of Euclidean spaces, including for instance rotations, reflections, scaling or shearing. In the second part of this talk we take an alternative viewpoint, considering passive gauge transformations of the labeling/coordinatization of data instead of active transformations of the data itself. This viewpoint allows us to generalize convolutions to Riemannian manifolds, which do not admit a canonical choice of reference frames (gauges) and thus require gauge equivariant convolution kernels. While only being designed to be locally gauge equivariant, we show that such coordinate independent convolutions are in fact equivariant w.r.t. the isometries of the manifold.


Maurice Weiler is a machine learning researcher with a focus on geometric and equivariant deep learning. After studying computational and theoretical physics at Heidelberg University, he is now a fourth year PhD student with Max Welling at AMLab, University of Amsterdam.