Clifford-Steerable Convolutional Neural Networks

Code

• github.com/maxxxzdn/clifford-group-equivariant-cnns
  OfficialIn paperjax★ 54

Abstract

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 R^3 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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