@inproceedings{
sonoda2023deep,
title={Deep Ridgelet Transform: Voice with Koopman Operator Constructively Proves Universality of Formal Deep Networks},
author={Sho Sonoda and Yuka Hashimoto and Isao Ishikawa and Masahiro Ikeda},
booktitle={NeurIPS 2023 Workshop on Symmetry and Geometry in Neural Representations},
year={2023},
url={https://openreview.net/forum?id=2EuaV9an6m}
}
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.
Deep Ridgelet Transform: Voice with Koopman Operator Constructively Proves Universality of Formal Deep Networks
Sho Sonoda Yuka Hashimoto Isao Ishikawa Masahiro Ikeda