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 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.