Clifford-Steerable Convolutional Neural Networks
Maksim Zhdanov David Ruhe Maurice Weiler Ana Lucic Johannes Brandstetter Patrick Forré
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.