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 cover, for instance, E (3) -equivariance on R³ and Poincar\'e-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.