On deep learning compression through superoscillations with application to risk theory

In this note, we show that redundancy in the number of neurons in a hidden layer of an artificial neural network with a holomorphic activation function can be effectively reduced without altering the network's architecture. This is done by replacing the trained weights of the given layer with the coefficients of superoscillations—band-limited functions that locally oscillate at frequencies exceeding their highest Fourier component. We examine the performance of such a model and its application to risk theory. The result establishes a link between deep learning optimization and the mathematical properties of superoscillations.