How Jellyfish Characterise Alternating Group Equivariant Neural Networks

Edward Pearce-Crump
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:27483-27495, 2023.

Abstract

We provide a full characterisation of all of the possible alternating group ($A_n$) equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$. In particular, we find a basis of matrices for the learnable, linear, $A_n$–equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-pearce-crump23b, title = {How Jellyfish Characterise Alternating Group Equivariant Neural Networks}, author = {Pearce-Crump, Edward}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {27483--27495}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/pearce-crump23b/pearce-crump23b.pdf}, url = {https://proceedings.mlr.press/v202/pearce-crump23b.html}, abstract = {We provide a full characterisation of all of the possible alternating group ($A_n$) equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$. In particular, we find a basis of matrices for the learnable, linear, $A_n$–equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.} }
Endnote
%0 Conference Paper %T How Jellyfish Characterise Alternating Group Equivariant Neural Networks %A Edward Pearce-Crump %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-pearce-crump23b %I PMLR %P 27483--27495 %U https://proceedings.mlr.press/v202/pearce-crump23b.html %V 202 %X We provide a full characterisation of all of the possible alternating group ($A_n$) equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$. In particular, we find a basis of matrices for the learnable, linear, $A_n$–equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.
APA
Pearce-Crump, E.. (2023). How Jellyfish Characterise Alternating Group Equivariant Neural Networks. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:27483-27495 Available from https://proceedings.mlr.press/v202/pearce-crump23b.html.

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