Poster
in
Workshop: Symmetry and Geometry in Neural Representations

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

Sho Sonoda ⋅ Yuka Hashimoto ⋅ Isao Ishikawa ⋅ Masahiro Ikeda

Project Page [ OpenReview]

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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