دانلود کتاب جنبه های ریاضی یادگیری عمیق

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.
We currently are witnessing the spectacular success of “deep learning” in both science (for example, in astronomy, biology, and medicine) and the public sector, where autonomous vehicles and robots are already present in daily life. However, the development of a rigorous mathematical foundation for deep learning is at an early stage, and most of the related research is still empirically driven. At the same time, methods based on deep neural networks have already shown their impressive potential in mathematical research areas such as imaging sciences, inverse problems, and the numerical analysis of partial differential equations, sometimes far outperforming classical mathematical approaches for particular classes of problem. This book provides the first comprehensive introduction to the subject, highlighting recent theoretical advances as well as outlining the numerous remaining research challenges.