Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations.

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any Hölder smooth function up to a given approximation error in Hölder norms in such a way that all weights of this neural network are bounded by 1. The latter feature is essential to control generalization errors in many statistical and machine learning applications.

A versatile deep-neural-network-based music preprocessing and remixing scheme for cochlear implant listeners.

While cochlear implants (CIs) have proven to restore speech perception to a remarkable extent, access to music remains difficult for most CI users. In this work, a methodology for the design of deep learning-based signal preprocessing strategies that simplify music signals and emphasize rhythmic information is proposed. It combines harmonic/percussive source separation and deep neural network (DNN) based source separation in a versatile source mixture model.