![[International Conference on Machine Learning Logo]](/image.pl?url=https%3a%2f%2fproceedings.mlr.press%2fv202%2fassets%2fimages%2flogo-pmlr.svg&f=jpg&w=240)
[edit]
How Jellyfish Characterise Alternating Group Equivariant Neural Networks
Edward Pearce-CrumpProceedings 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, inProceedings of Machine Learning Research 202:27483-27495 Available from https://proceedings.mlr.press/v202/pearce-crump23b.html.