{"id":1039245,"date":"2024-05-22T15:22:45","date_gmt":"2024-05-22T22:22:45","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=1039245"},"modified":"2024-05-22T15:22:45","modified_gmt":"2024-05-22T22:22:45","slug":"clifford-steerable-convolutional-neural-networks","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/clifford-steerable-convolutional-neural-networks\/","title":{"rendered":"Clifford-Steerable Convolutional Neural Networks"},"content":{"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. 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. We significantly and 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