We describe the new field of mathematical analysis of deep learning. This field emerged around a list
of research questions that were not answered within the classical framework of learning theory. These
questions concern: the outstanding generalization power of overparametrized neural networks, the role of
depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful
optimization performance despite the non-convexity of the problem, understanding what features are
learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects
of an architecture affect the behavior of a learning task in which way. We present an overview of modern
approaches that yield partial answers to these questions. For selected approaches, we describe the main
ideas in more detail. Read More

#deep-learning