Clifford-Steerable Convolutional Neural Networks

Maksim Zhdanov, David Ruhe, Maurice Weiler, Ana Lucic, Johannes Brandstetter, Patrick Forré
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:61203-61228, 2024.

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 this Paper

BibTeX
@InProceedings{pmlr-v235-zhdanov24a, title = {Clifford-Steerable Convolutional Neural Networks}, author = {Zhdanov, Maksim and Ruhe, David and Weiler, Maurice and Lucic, Ana and Brandstetter, Johannes and Forr\'{e}, Patrick}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {61203--61228}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/zhdanov24a/zhdanov24a.pdf}, url = {https://proceedings.mlr.press/v235/zhdanov24a.html}, 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.} }
Endnote
%0 Conference Paper %T Clifford-Steerable Convolutional Neural Networks %A Maksim Zhdanov %A David Ruhe %A Maurice Weiler %A Ana Lucic %A Johannes Brandstetter %A Patrick Forré %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-zhdanov24a %I PMLR %P 61203--61228 %U https://proceedings.mlr.press/v235/zhdanov24a.html %V 235 %X 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.
APA
Zhdanov, M., Ruhe, D., Weiler, M., Lucic, A., Brandstetter, J. & Forré, P.. (2024). Clifford-Steerable Convolutional Neural Networks. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:61203-61228 Available from https://proceedings.mlr.press/v235/zhdanov24a.html.

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