Equivariance Through Parameter-Sharing

Siamak Ravanbakhsh, Jeff Schneider, Barnabás Póczos
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:2892-2901, 2017.

Abstract

We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group G that acts discretely on the input and output of a standard neural network layer, we show that its equivariance is linked to the symmetry group of network parameters. We then propose two parameter-sharing scheme to induce the desirable symmetry on the parameters of the neural network. Under some conditions on the action of G, our procedure for tying the parameters achieves G-equivariance and guarantees sensitivity to all other permutation groups outside of G.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-ravanbakhsh17a, title = {Equivariance Through Parameter-Sharing}, author = {Siamak Ravanbakhsh and Jeff Schneider and Barnab{\'a}s P{\'o}czos}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {2892--2901}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/ravanbakhsh17a/ravanbakhsh17a.pdf}, url = {https://proceedings.mlr.press/v70/ravanbakhsh17a.html}, abstract = {We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group G that acts discretely on the input and output of a standard neural network layer, we show that its equivariance is linked to the symmetry group of network parameters. We then propose two parameter-sharing scheme to induce the desirable symmetry on the parameters of the neural network. Under some conditions on the action of G, our procedure for tying the parameters achieves G-equivariance and guarantees sensitivity to all other permutation groups outside of G.} }
Endnote
%0 Conference Paper %T Equivariance Through Parameter-Sharing %A Siamak Ravanbakhsh %A Jeff Schneider %A Barnabás Póczos %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-ravanbakhsh17a %I PMLR %P 2892--2901 %U https://proceedings.mlr.press/v70/ravanbakhsh17a.html %V 70 %X We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group G that acts discretely on the input and output of a standard neural network layer, we show that its equivariance is linked to the symmetry group of network parameters. We then propose two parameter-sharing scheme to induce the desirable symmetry on the parameters of the neural network. Under some conditions on the action of G, our procedure for tying the parameters achieves G-equivariance and guarantees sensitivity to all other permutation groups outside of G.
APA
Ravanbakhsh, S., Schneider, J. & Póczos, B.. (2017). Equivariance Through Parameter-Sharing. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:2892-2901 Available from https://proceedings.mlr.press/v70/ravanbakhsh17a.html.

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