Clifford-Steerable Convolutional Neural Networks

Abstract

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of $\mathrm{E}(p,q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They cover, for instance, $\mathrm{E}(3)$-equivariance on $\mathbb{R}^3$ and Poincaré-equivariance on Minkowski spacetime $\mathbb{R}^{1,3}$. Our approach is based on an implicit parametrization of $\mathrm{O}(p,q)$-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.

Maurice Weiler

Deep Learning Researcher

I’m a researcher working on geometric and equivariant deep learning.