UAI 2021poster46 citations
Improved generalization bounds of group invariant / equivariant deep networks via quotient feature spaces
Akiyoshi Sannai, Masaaki Imaizumi, Makoto Kawano
Abstract
Numerous invariant (or equivariant) neural networks have succeeded in handling the invariant data such as point clouds and graphs. However, a generalization theory for the neural networks has not been well developed, because several essential factors for the theory, such as network size and margin distribution, are not deeply connected to the invariance and equivariance. In this study, we develop a novel generalization error bound for invariant and equivariant deep neural networks. To describe the effect of invariance and equivariance on generalization, we develop a notion of a
BibTeX
@InProceedings{pmlr-v161-sannai21a,
title = {Improved generalization bounds of group invariant / equivariant deep networks via quotient feature spaces},
author = {Sannai, Akiyoshi and Imaizumi, Masaaki and Kawano, Makoto},
booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence},
pages = {771--780},
year = {2021},
editor = {de Campos, Cassio and Maathuis, Marloes H.},
volume = {161},
series = {Proceedings of Machine Learning Research},
month = {27--30 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v161/sannai21a/sannai21a.pdf},
url = {https://proceedings.mlr.press/v161/sannai21a.html},
abstract = {Numerous invariant (or equivariant) neural networks have succeeded in handling the invariant data such as point clouds and graphs. However, a generalization theory for the neural networks has not been well developed, because several essential factors for the theory, such as network size and margin distribution, are not deeply connected to the invariance and equivariance. In this study, we develop a novel generalization error bound for invariant and equivariant deep neural networks. To describe the effect of invariance and equivariance on generalization, we develop a notion of a