Neural networks (NNs) are the method of choice for building learning algorithms. They are
now being investigated for other numerical tasks such as solving high-dimensional partial …

Artificial neural networks (ANNs) have very successfully been used in numerical simulations
for a series of computational problems ranging from image classification/image recognition …

We derive fundamental lower bounds on the connectivity and the memory requirements of
deep neural networks guaranteeing uniform approximation rates for arbitrary function …

The development of new classification and regression algorithms based on empirical risk
minimization (ERM) over deep neural network hypothesis classes, coined deep learning …

In this survey we discuss various approximation-theoretic problems that arise in the
multilayer feedforward perceptron (MLP) model in neural networks. The MLP model is one of …

This paper develops fundamental limits of deep neural network learning by characterizing
what is possible if no constraints are imposed on the learning algorithm and on the amount …

Single hidden-layer feedforward neural networks have been proposed as an approach to by-
pass the curse of dimensionality and are now becoming widely applied to approximation or …

In recent years deep artificial neural networks (DNNs) have been successfully employed in
numerical simulations for a multitude of computational problems including, for example …

We study the expressivity of deep neural networks. Measuring a network's complexity by its
number of connections or by its number of neurons, we consider the class of functions for …

This paper develops fundamental limits of deep neural network learning by characterizing
what is possible if no constraints are imposed on the learning algorithm and on the amount …