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 (An) equivariant neural networks whose layers are some tensor power of Rn. In particular, we find a basis of matrices for the learnable, linear, An–equivariant layer functions between such tensor power spaces in the standard basis of Rn. 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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