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arXiv · 2310.03529

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

Sho Sonoda·Yuka Hashimoto·Isao Ishikawa·Masahiro Ikeda
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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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Sho Sonoda, Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda. 2023-10-05. Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks. https://arxiv.org/abs/2310.03529

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