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This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures…

This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural…

This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks, the theory…

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…

"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…

This survey provides an in-depth and explanatory review of the approximation properties of deep neural networks, with a focus on feed-forward and residual architectures. The primary objective is to examine how effectively neural networks…

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the…

This book provides a comprehensive introduction to the foundational concepts of machine learning (ML) and deep learning (DL). It bridges the gap between theoretical mathematics and practical application, focusing on Python as the primary…

The scope of this teaching package is to make a brief induction to Artificial Neural Networks (ANNs) for people who have no previous knowledge of them. We first make a brief introduction to models of networks, for then describing in general…

This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

Artificial neural networks (ANN), typically referred to as neural networks, are a class of Machine Learning algorithms and have achieved widespread success, having been inspired by the biological structure of the human brain. Neural…

Learning algorithms related to artificial neural networks and in particular for Deep Learning may seem to involve many bells and whistles, called hyper-parameters. This chapter is meant as a practical guide with recommendations for some of…

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

Artificial neural networks (ANNs) are essential tools in machine learning that have drawn increasing attention in neuroscience. Besides offering powerful techniques for data analysis, ANNs provide a new approach for neuroscientists to build…

Activation functions shape the outputs of artificial neurons and, therefore, are integral parts of neural networks in general and deep learning in particular. Some activation functions, such as logistic and relu, have been used for many…

Originally inspired by neurobiology, deep neural network models have become a powerful tool of machine learning and artificial intelligence, where they are used to approximate functions and dynamics by learning from examples. Here we give a…

Recent times are witnessing rapid development in machine learning algorithm systems, especially in reinforcement learning, natural language processing, computer and robot vision, image processing, speech, and emotional processing and…

This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the…

This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as…