Papers › Clifford-Steerable Convolutional Neural Networks

Clifford-Steerable Convolutional Neural Networks

22 Feb 2024arXiv:2402.14730archive 2025-07-28

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 E(p, q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces ℝ^(p,q). They cover, for instance, E(3)-equivariance on ℝ³ and Poincar\'e-equivariance on Minkowski spacetime ℝ^(1,3). Our approach is based on an implicit parametrization of 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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