Mathematical Aspects of Deep Learning

Description

In recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves both as a starting point for researchers and graduate students in computer science, mathematics, and statistics trying to get into the field and as an invaluable reference for future research. Frontmatter Contents Contributors Preface 1 The Modern Mathematics of Deep Learning 2 Generalization in Deep Learning 3 Expressivity of Deep Neural Networks 4 Optimization Landscape of Neural Networks 5 Explaining the Decisions of Convolutional and Recurrent Neural Networks 6 Stochastic Feedforward Neural Networks: Universal Approximation 7 Deep Learning as Sparsity-Enforcing Algorithms 8 The Scattering Transform 9 Deep Generative Models and Inverse Problems 10 Dynamical Systems and Optimal Control Approach to Deep Learning 11 Bridging Many-Body Quantum Physics and Deep Learning via Tensor Networks