Clifford-Steerable Convolutional Neural Networks

Abstract

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of ${\operatorname{E}}(p, q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They specialize, for instance, to ${\operatorname{E}}(3)$-equivariance on $\mathbb{R}^3$ and Poincaré-equivariance on Minkowski spacetime $\mathbb{R}^{1,3}$. Our approach is based on an implicit parametrization of ${\operatorname{O}}(p,q)$-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.

Cite

Text

Zhdanov et al. "Clifford-Steerable Convolutional Neural Networks." International Conference on Machine Learning, 2024.

Markdown

[Zhdanov et al. "Clifford-Steerable Convolutional Neural Networks." International Conference on Machine Learning, 2024.](https://mlanthology.org/icml/2024/zhdanov2024icml-cliffordsteerable/)

BibTeX

@inproceedings{zhdanov2024icml-cliffordsteerable,
  title     = {{Clifford-Steerable Convolutional Neural Networks}},
  author    = {Zhdanov, Maksim and Ruhe, David and Weiler, Maurice and Lucic, Ana and Brandstetter, Johannes and Forré, Patrick},
  booktitle = {International Conference on Machine Learning},
  year      = {2024},
  pages     = {61203-61228},
  volume    = {235},
  url       = {https://mlanthology.org/icml/2024/zhdanov2024icml-cliffordsteerable/}
}