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.<\/p>\n","protected":false},"excerpt":{"rendered":"
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. 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