Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks
Machine Learning
2023-11-14 v2 Machine Learning
Abstract
We identify hidden layers inside a deep neural network (DNN) with group actions on the data domain, and formulate a formal deep network as a dual voice transform with respect to the Koopman operator, a linear representation of the group action. Based on the group theoretic arguments, particularly by using Schur's lemma, we show a simple proof of the universality of DNNs.
Keywords
Cite
@article{arxiv.2310.03529,
title = {Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks},
author = {Sho Sonoda and Yuka Hashimoto and Isao Ishikawa and Masahiro Ikeda},
journal= {arXiv preprint arXiv:2310.03529},
year = {2023}
}
Comments
NeurReps 2023