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arXiv · 2402.14730

Clifford-Steerable Convolutional Neural Networks

Maksim Zhdanov·David Ruhe·Maurice Weiler·Ana Lucic·Johannes Brandstetter·Patrick Forré
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Abstract

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.

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Maksim Zhdanov, David Ruhe, Maurice Weiler, Ana Lucic, Johannes Brandstetter, Patrick Forré. 2024-02-22. Clifford-Steerable Convolutional Neural Networks. https://arxiv.org/abs/2402.14730

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