Clifford-Steerable Convolutional Neural Networks
Maksim Zhdanov, David Ruhe, Maurice Weiler, Ana Lucic, Johannes Brandstetter, Patrick Forré
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.
BibTeX
@inproceedings{
zhdanov2024cliffordsteerable,
title={Clifford-Steerable Convolutional Neural Networks},
author={Maksim Zhdanov and David Ruhe and Maurice Weiler and Ana Lucic and Johannes Brandstetter and Patrick Forr{\'e}},
booktitle={Forty-first International Conference on Machine Learning},
year={2024},
url={https://openreview.net/forum?id=XTglHJjzQI}
}