Deep Neural Networks in a Mathematical Framework PDF Download
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Author: Anthony L. Caterini
Publisher: Springer
ISBN: 3319753045
Category : Computers
Languages : en
Pages : 95
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Book Description
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.
Author: Anthony L. Caterini
Publisher: Springer
ISBN: 3319753045
Category : Computers
Languages : en
Pages : 95
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Book Description
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.
Author: Changliu Liu
Publisher:
ISBN: 9781680837865
Category :
Languages : en
Pages :
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Book Description
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.
Author: Richard M. Golden
Publisher: MIT Press
ISBN: 9780262071741
Category : Computers
Languages : en
Pages : 452
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Book Description
For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.
Author: Krishnendu Chaudhury
Publisher: Simon and Schuster
ISBN: 1617296481
Category : Computers
Languages : en
Pages : 550
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Book Description
Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. You'll peer inside the "black box" to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. Math and Architectures of Deep Learning sets out the foundations of DL usefully and accessibly to working practitioners. Each chapter explores a new fundamental DL concept or architectural pattern, explaining the underpinning mathematics and demonstrating how they work in practice with well-annotated Python code. You'll start with a primer of basic algebra, calculus, and statistics, working your way up to state-of-the-art DL paradigms taken from the latest research. Learning mathematical foundations and neural network architecture can be challenging, but the payoff is big. You'll be free from blind reliance on pre-packaged DL models and able to build, customize, and re-architect for your specific needs. And when things go wrong, you'll be glad you can quickly identify and fix problems.
Author: Daniel A. Roberts
Publisher: Cambridge University Press
ISBN: 1316519333
Category : Computers
Languages : en
Pages : 473
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Book Description
This volume develops an effective theory approach to understanding deep neural networks of practical relevance.
Author: Mehryar Mohri
Publisher: MIT Press
ISBN: 0262351366
Category : Computers
Languages : en
Pages : 505
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Book Description
A new edition of a graduate-level machine learning textbook that focuses on the analysis and theory of algorithms. This book is a general introduction to machine learning that can serve as a textbook for graduate students and a reference for researchers. It covers fundamental modern topics in machine learning while providing the theoretical basis and conceptual tools needed for the discussion and justification of algorithms. It also describes several key aspects of the application of these algorithms. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning is unique in its focus on the analysis and theory of algorithms. The first four chapters lay the theoretical foundation for what follows; subsequent chapters are mostly self-contained. Topics covered include the Probably Approximately Correct (PAC) learning framework; generalization bounds based on Rademacher complexity and VC-dimension; Support Vector Machines (SVMs); kernel methods; boosting; on-line learning; multi-class classification; ranking; regression; algorithmic stability; dimensionality reduction; learning automata and languages; and reinforcement learning. Each chapter ends with a set of exercises. Appendixes provide additional material including concise probability review. This second edition offers three new chapters, on model selection, maximum entropy models, and conditional entropy models. New material in the appendixes includes a major section on Fenchel duality, expanded coverage of concentration inequalities, and an entirely new entry on information theory. More than half of the exercises are new to this edition.
Author: Zhengyan Lin
Publisher: Springer Science & Business Media
ISBN: 3642052614
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.
Author: Dong Eui Chang
Publisher: Springer
ISBN: 1493924419
Category : Mathematics
Languages : en
Pages : 506
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Book Description
This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.
Author: Ovidiu Calin
Publisher: Springer Nature
ISBN: 3030367215
Category : Mathematics
Languages : en
Pages : 760
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Book Description
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.
Author: Giuseppe Ciaburro
Publisher: Packt Publishing Ltd
ISBN: 1788399412
Category : Computers
Languages : en
Pages : 264
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Book Description
Uncover the power of artificial neural networks by implementing them through R code. About This Book Develop a strong background in neural networks with R, to implement them in your applications Build smart systems using the power of deep learning Real-world case studies to illustrate the power of neural network models Who This Book Is For This book is intended for anyone who has a statistical background with knowledge in R and wants to work with neural networks to get better results from complex data. If you are interested in artificial intelligence and deep learning and you want to level up, then this book is what you need! What You Will Learn Set up R packages for neural networks and deep learning Understand the core concepts of artificial neural networks Understand neurons, perceptrons, bias, weights, and activation functions Implement supervised and unsupervised machine learning in R for neural networks Predict and classify data automatically using neural networks Evaluate and fine-tune the models you build. In Detail Neural networks are one of the most fascinating machine learning models for solving complex computational problems efficiently. Neural networks are used to solve wide range of problems in different areas of AI and machine learning. This book explains the niche aspects of neural networking and provides you with foundation to get started with advanced topics. The book begins with neural network design using the neural net package, then you'll build a solid foundation knowledge of how a neural network learns from data, and the principles behind it. This book covers various types of neural network including recurrent neural networks and convoluted neural networks. You will not only learn how to train neural networks, but will also explore generalization of these networks. Later we will delve into combining different neural network models and work with the real-world use cases. By the end of this book, you will learn to implement neural network models in your applications with the help of practical examples in the book. Style and approach A step-by-step guide filled with real-world practical examples.
