Brauer’s Group Equivariant Neural Networks
Abstract
We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$ for three symmetry groups that are missing from the machine learning literature: $O(n)$, the orthogonal group; $SO(n)$, the special orthogonal group; and $Sp(n)$, the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$ when the group is $O(n)$ or $SO(n)$, and in the symplectic basis of $\mathbb{R}^{n}$ when the group is $Sp(n)$.
Cite
Text
Pearce-Crump. "Brauer’s Group Equivariant Neural Networks." International Conference on Machine Learning, 2023.Markdown
[Pearce-Crump. "Brauer’s Group Equivariant Neural Networks." International Conference on Machine Learning, 2023.](https://mlanthology.org/icml/2023/pearcecrump2023icml-brauers/)BibTeX
@inproceedings{pearcecrump2023icml-brauers,
title = {{Brauer’s Group Equivariant Neural Networks}},
author = {Pearce-Crump, Edward},
booktitle = {International Conference on Machine Learning},
year = {2023},
pages = {27461-27482},
volume = {202},
url = {https://mlanthology.org/icml/2023/pearcecrump2023icml-brauers/}
}