ML Anthology

Deep Ridgelet Transform: Voice with Koopman Operator Constructively Proves Universality of Formal Deep Networks

Sho Sonoda, Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda
NeurIPSW 2023
/neuripsw/2023/sonoda2023neuripsw-deep/

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.

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Cite

Text

Sonoda et al. "Deep Ridgelet Transform: Voice with Koopman Operator Constructively Proves Universality of Formal Deep Networks." NeurIPS 2023 Workshops: NeurReps, 2023.

Markdown

[Sonoda et al. "Deep Ridgelet Transform: Voice with Koopman Operator Constructively Proves Universality of Formal Deep Networks." NeurIPS 2023 Workshops: NeurReps, 2023.](https://mlanthology.org/neuripsw/2023/sonoda2023neuripsw-deep/)

BibTeX

@inproceedings{sonoda2023neuripsw-deep,
  title     = {{Deep Ridgelet Transform: Voice with Koopman Operator Constructively Proves Universality of Formal Deep Networks}},
  author    = {Sonoda, Sho and Hashimoto, Yuka and Ishikawa, Isao and Ikeda, Masahiro},
  booktitle = {NeurIPS 2023 Workshops: NeurReps},
  year      = {2023},
  url       = {https://mlanthology.org/neuripsw/2023/sonoda2023neuripsw-deep/}
}