Title: On Generalization and Regularization in Deep Learning,
Abstract: Why do large neural network generalize so well on complex tasks such as image
classification or speech recognition? What exactly is the role regularization
for them? These are arguably among the most important open questions in machine
learning today. In a recent and thought provoking paper [C. Zhang et al.]
several authors performed a number of numerical experiments that hint at the
need for novel theoretical concepts to account for this phenomenon. The paper
stirred quit a lot of excitement among the machine learning community but at
the same time it created some confusion as discussions on OpenReview.net
testifies. The aim of this pedagogical paper is to make this debate accessible
to a wider audience of data scientists without advanced theoretical knowledge
in statistical learning. The focus here is on explicit mathematical definitions
and on a discussion of relevant concepts, not on proofs for which we provide
references.