Deep learning is usually described as an experiment-driven field under continuous criticizes
of lacking theoretical foundations. This problem has been partially fixed by a large volume of …

This textbook establishes a theoretical framework for understanding deep learning models
of practical relevance. With an approach that borrows from theoretical physics, Roberts and …

A grand challenge in machine learning is the development of computational algorithms that
match or outperform humans in perceptual inference tasks that are complicated by nuisance …

This book offers a comprehensive introduction to the central ideas that underpin deep
learning. It is intended both for newcomers to machine learning and for those already …

This paper analyzes the rapid and unexpected rise of deep learning within Artificial
Intelligence and its applications. It tackles the possible reasons for this remarkable success …

Abstract Machine learning is increasingly targeting areas where input data cannot be
accurately described by a single vector, but can be modeled instead using the more flexible …

Abstract Recent works (eg,(Li\& Arora, 2020)) suggest that the use of popular normalization
schemes (including Batch Normalization) in today's deep learning can move it far from a …

Stochastic Gradient Descent (SGD) and its variants are mainstream methods for training
deep networks in practice. SGD is known to find a flat minimum that often generalizes well …

We describe an approach to understand the peculiar and counterintuitive generalization
properties of deep neural networks. The approach involves going beyond worst-case …

The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …