Clifford-Steerable Convolutional Neural Networks - Zhdanov, Maksim; Ruhe, David; Weiler, Maurice; Lucic, Ana; Brandstetter, Johannes; Forr'e, Patrick (ICML 2024, 2024)
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 [R]^3 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.