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.

翻译：我们提出克利福德可导向卷积神经网络（CS-CNNs），这是一类新型的$\mathrm{E}(p, q)$-等变CNN。CS-CNNs处理伪欧几里得空间$\mathbb{R}^{p,q}$上的多重向量场，涵盖例如$\mathbb{R}^3$上的$\mathrm{E}(3)$-等变性以及闵可夫斯基时空$\mathbb{R}^{1,3}$上的庞加莱等变性。该方法通过克利福德群等变神经网络对$\mathrm{O}(p,q)$-可导向核进行隐式参数化。在流体动力学及相对论电动力学预测任务中，我们显著且稳定地超越了基线方法。