Skip to yearly menu bar Skip to main content

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


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.

Chat is not available.