Clifford-Steerable Convolutional Neural Networks
<|reference_start|>Clifford-Steerable Convolutional Neural Networks: We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of $\mathrm{E}(p, q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They cover, for instance, $\mathrm{E}(3)$-equivariance on $\mathbb{R}^3$ and Poincar\'e-equivariance on Minkowski spacetime $\mathbb{R}^{1,3}$. Our approach is based on an implicit parametrization of $\mathrm{O}(p,q)$-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.<|reference_end|>
@article{zhdanov2024clifford-steerable,
    title={Clifford-Steerable Convolutional Neural Networks},
    author={Maksim Zhdanov, David Ruhe, Maurice Weiler, Ana Lucic, Johannes
  Brandstetter, Patrick Forr'e},
    journal={arXiv preprint arXiv:2402.14730},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.14730},
    primaryClass={cs.LG cs.AI}
}