Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks
This provides a theoretical foundation for deep learning by addressing the universality problem for researchers in machine learning, though it appears incremental as it builds on existing group-theoretic frameworks.
The paper tackles the problem of proving the universality of deep neural networks by identifying hidden layers with group actions and formulating them as a dual voice transform using the Koopman operator, resulting in a simple proof based on group theory and Schur's lemma.
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.