Mathematical Aspects of Deep Learning

The development of new classification and regression algorithms based on deep learning has revolutionized AI, machine learning, and data analysis. This book provides a theoretical foundation to guarantee the success of these algorithms and serves as a reference for researchers and graduate students.

Format: Hardback
Length: 492 pages
Publication date: 22 December 2022
Publisher: Cambridge University Press

In recent years, the emergence of novel classification and regression algorithms fueled by deep learning has sparked a transformative revolution in the realms of artificial intelligence, machine learning, and data analysis. The establishment of a theoretical framework to ensure the efficacy of these algorithms has emerged as one of the most dynamic and captivating research endeavors in applied mathematics. This comprehensive book offers a comprehensive and authoritative account of the current mathematical understanding of deep learning techniques, presented by the foremost experts in the field. Serving as a valuable resource for both aspiring researchers and graduate students seeking to foray into the field, as well as a steadfast companion for future research endeavors, this text provides a deep dive into the intricate mechanisms and applications of deep learning.

The advent of deep learning has revolutionized the field of artificial intelligence, machine learning, and data analysis. These algorithms have achieved remarkable results in various domains, such as image recognition, natural language processing, and autonomous driving. However, the success of deep learning relies on developing a theoretical foundation that guarantees its effectiveness. This book aims to provide a comprehensive and up-to-date overview of the mathematical foundations of deep learning, covering topics such as neural networks, optimization, and machine learning theory.

Neural networks are the core building blocks of deep learning. They are modeled as a collection of interconnected neurons that process input data and generate output predictions. The optimization algorithms used in deep learning are designed to minimize the loss function, which measures the difference between the predicted output and the actual output. Machine learning theory is a fundamental concept that underpins deep learning. It involves the use of statistical models to learn from data and make predictions.

This book is written for researchers and graduate students in computer science, mathematics, and statistics who are interested in learning about the mathematical foundations of deep learning. It provides a comprehensive introduction to the field, covering the key concepts and techniques in a clear and concise manner. The book is organized into four chapters, each covering a different aspect of the mathematical foundations of deep learning.

Chapter 1 introduces neural networks and their basic properties. It covers topics such as activation functions, weight initialization, and backpropagation. Chapter 2 discusses optimization algorithms used in deep learning, including gradient descent, stochastic gradient descent, and Adam optimization. Chapter 3 explores machine learning theory, including supervised learning, unsupervised learning, and reinforcement learning. Chapter 4 discusses the application of deep learning in various domains, such as image recognition, natural language processing, and autonomous driving.

In conclusion, 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 establishment 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.

Weight: 1076g
Dimension: 177 x 250 x 29 (mm)
ISBN-13: 9781316516782