Clifford-Steerable Convolutional Neural Networks

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 Poincar\’e-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.