Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 23 of its 48 references that are in the map. First posted on arXiv 5 Oct 2023.
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23 of 48 references.
References · 23
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11 more
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Citing papers per year: 2024: 2.
2 papers.