Clifford-steerable convolutional neural networks

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 R^p,q. They specialize, for instance, to E(3)-equivariance on R3 and Poincaré-equivariance on Minkowski spacetime R^1,3. 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.