Clifford-Steerable CNNs

Topic: Clifford-Steerable Convolutional Neural Networks

Abstract:

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p,q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces ℝp,q. They cover, for instance, E(3)-equivariance on ℝ3 and Poincaré-equivariance on Minkowski spacetime ℝ1,3. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

Speaker(s):

Maksim Zhdanov is a PhD student at the AMLab, University of Amsterdam (UvA) supervised by Max Welling, Jan-Willem van de Meent, and Alfons Hoekstra. Previously, he completed his MSc in computer science from TU Dresden. Before that, he studied physics at the Saint Petersburg State University. His research interests include physics-inspired deep learning, geometric deep learning, and scientific machine learning.