Deep Neural Networks In A Mathematical Framework

This SpringerBrief describes how to build a rigorous end-to-end mathematical framework for deep neural networks. The authors provide tools to represent and describe neural networks, casting previous results in the field in a more natural light. In particular, the authors derive gradient descent algorithms in a unified way for several neural network structures, including multilayer perceptrons, convolutional neural networks, deep autoencoders and recurrent neural networks. Furthermore, the authors developed framework is both more concise and mathematically intuitive than previous representations of neural networks. This SpringerBrief is one step towards unlocking the black box of Deep Learning. The authors believe that this framework will help catalyze further discoveries regarding the mathematical properties of neural networks.This SpringerBrief is accessible not only to researchers, professionals and students working and studying in the field of deep learning, but also to those outside of the neutral network community.

A comprehensive guide to getting well-versed with the mathematical techniques for building modern deep learning architectures Key FeaturesUnderstand linear algebra, calculus, gradient algorithms, and other concepts essential for training deep neural networksLearn the mathematical concepts needed to understand how deep learning models functionUse deep learning for solving problems related to vision, image, text, and sequence applicationsBook Description Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL. What you will learnUnderstand the key mathematical concepts for building neural network modelsDiscover core multivariable calculus conceptsImprove the performance of deep learning models using optimization techniquesCover optimization algorithms, from basic stochastic gradient descent (SGD) to the advanced Adam optimizerUnderstand computational graphs and their importance in DLExplore the backpropagation algorithm to reduce output errorCover DL algorithms such as convolutional neural networks (CNNs), sequence models, and generative adversarial networks (GANs)Who this book is for This book is for data scientists, machine learning developers, aspiring deep learning developers, or anyone who wants to understand the foundation of deep learning by learning the math behind it. Working knowledge of the Python programming language and machine learning basics is required.

This book covers a large set of methods in the field of Artificial Intelligence - Deep Learning applied to real-world problems. The fundamentals of the Deep Learning approach and different types of Deep Neural Networks (DNNs) are first summarized in this book, which offers a comprehensive preamble for further problem–oriented chapters. The most interesting and open problems of machine learning in the framework of Deep Learning are discussed in this book and solutions are proposed. This book illustrates how to implement the zero-shot learning with Deep Neural Network Classifiers, which require a large amount of training data. The lack of annotated training data naturally pushes the researchers to implement low supervision algorithms. Metric learning is a long-term research but in the framework of Deep Learning approaches, it gets freshness and originality. Fine-grained classification with a low inter-class variability is a difficult problem for any classification tasks. This book presents how it is solved, by using different modalities and attention mechanisms in 3D convolutional networks. Researchers focused on Machine Learning, Deep learning, Multimedia and Computer Vision will want to buy this book. Advanced level students studying computer science within these topic areas will also find this book useful.

Neural networks have been widely used in many applications, such as image classification and understanding, language processing, and control of autonomous systems. These networks work by mapping inputs to outputs through a sequence of layers. At each layer, the input to that layer undergoes an affine transformation followed by a simple nonlinear transformation before being passed to the next layer. Neural networks are being used for increasingly important tasks, and in some cases, incorrect outputs can lead to costly consequences, hence validation of correctness at each layer is vital. The sheer size of the networks makes this not feasible using traditional methods. In this monograph, the authors survey a class of methods that are capable of formally verifying properties of deep neural networks. In doing so, they introduce a unified mathematical framework for verifying neural networks, classify existing methods under this framework, provide pedagogical implementations of existing methods, and compare those methods on a set of benchmark problems. Algorithms for Verifying Deep Neural Networks serves as a tutorial for students and professionals interested in this emerging field as well as a benchmark to facilitate the design of new verification algorithms.

Journey through the theory and practice of modern deep learning, and apply innovative techniques to solve everyday data problems. In Inside Deep Learning, you will learn how to: Implement deep learning with PyTorch Select the right deep learning components Train and evaluate a deep learning model Fine tune deep learning models to maximize performance Understand deep learning terminology Adapt existing PyTorch code to solve new problems Inside Deep Learning is an accessible guide to implementing deep learning with the PyTorch framework. It demystifies complex deep learning concepts and teaches you to understand the vocabulary of deep learning so you can keep pace in a rapidly evolving field. No detail is skipped—you’ll dive into math, theory, and practical applications. Everything is clearly explained in plain English. About the technology Deep learning doesn’t have to be a black box! Knowing how your models and algorithms actually work gives you greater control over your results. And you don’t have to be a mathematics expert or a senior data scientist to grasp what’s going on inside a deep learning system. This book gives you the practical insight you need to understand and explain your work with confidence. About the book Inside Deep Learning illuminates the inner workings of deep learning algorithms in a way that even machine learning novices can understand. You’ll explore deep learning concepts and tools through plain language explanations, annotated code, and dozens of instantly useful PyTorch examples. Each type of neural network is clearly presented without complex math, and every solution in this book can run using readily available GPU hardware! What's inside Select the right deep learning components Train and evaluate a deep learning model Fine tune deep learning models to maximize performance Understand deep learning terminology About the reader For Python programmers with basic machine learning skills. About the author Edward Raff is a Chief Scientist at Booz Allen Hamilton, and the author of the JSAT machine learning library. Table of Contents PART 1 FOUNDATIONAL METHODS 1 The mechanics of learning 2 Fully connected networks 3 Convolutional neural networks 4 Recurrent neural networks 5 Modern training techniques 6 Common design building blocks PART 2 BUILDING ADVANCED NETWORKS 7 Autoencoding and self-supervision 8 Object detection 9 Generative adversarial networks 10 Attention mechanisms 11 Sequence-to-sequence 12 Network design alternatives to RNNs 13 Transfer learning 14 Advanced building blocks

The subject of Neural Networks is being seen to be coming of age, after its initial inception 50 years ago in the seminal work of McCulloch and Pitts. It is proving to be valuable in a wide range of academic disciplines and in important applications in industrial and business tasks. The progress being made in each approach is considerable. Nevertheless, both stand in need of a theoretical framework of explanation to underpin their usage and to allow the progress being made to be put on a firmer footing. This book aims to strengthen the foundations in its presentation of mathematical approaches to neural networks. It is through these that a suitable explanatory framework is expected to be found. The approaches span a broad range, from single neuron details to numerical analysis, functional analysis and dynamical systems theory. Each of these avenues provides its own insights into the way neural networks can be understood, both for artificial ones and simplified simulations. As a whole, the publication underlines the importance of the ever-deepening mathematical understanding of neural networks.

Math for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits. With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network. In addition you’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta.

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.