Mathematical Perspectives On Neural Networks

Author : Paul Smolensky,Michael C. Mozer,David E. Rumelhart
Publisher : Psychology Press
Page : 890 pages
File Size : 47,5 Mb
Release : 2013-05-13
Category : Psychology
ISBN : 9781134773015

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Mathematical Perspectives on Neural Networks by Paul Smolensky,Michael C. Mozer,David E. Rumelhart Pdf

Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.

Author : Paul Smolensky,Michael C. Mozer,David E. Rumelhart
Publisher : Unknown
Page : 900 pages
File Size : 47,5 Mb
Release : 1996-05
Category : Computers
ISBN : 0805812024

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Mathematical Perspectives on Neural Networks by Paul Smolensky,Michael C. Mozer,David E. Rumelhart Pdf

Author : Martin Anthony
Publisher : SIAM
Page : 137 pages
File Size : 52,5 Mb
Release : 2001-01-01
Category : Computers
ISBN : 9780898714807

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Discrete Mathematics of Neural Networks by Martin Anthony Pdf

This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.

Author : Stephen W. Ellacott,John C. Mason,Iain J. Anderson
Publisher : Springer Science & Business Media
Page : 423 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461560999

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Mathematics of Neural Networks by Stephen W. Ellacott,John C. Mason,Iain J. Anderson Pdf

This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.

Author : Leonid Berlyand,Pierre-Emmanuel Jabin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 666 pages
File Size : 43,8 Mb
Release : 2023-04-27
Category : Computers
ISBN : 9783111025803

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Mathematics of Deep Learning by Leonid Berlyand,Pierre-Emmanuel Jabin Pdf

The goal of this book is to provide a mathematical perspective on some key elements of the so-called deep neural networks (DNNs). Much of the interest in deep learning has focused on the implementation of DNN-based algorithms. Our hope is that this compact textbook will offer a complementary point of view that emphasizes the underlying mathematical ideas. We believe that a more foundational perspective will help to answer important questions that have only received empirical answers so far. The material is based on a one-semester course Introduction to Mathematics of Deep Learning" for senior undergraduate mathematics majors and first year graduate students in mathematics. Our goal is to introduce basic concepts from deep learning in a rigorous mathematical fashion, e.g introduce mathematical definitions of deep neural networks (DNNs), loss functions, the backpropagation algorithm, etc. We attempt to identify for each concept the simplest setting that minimizes technicalities but still contains the key mathematics.

Author : Anthony L. Caterini,Dong Eui Chang
Publisher : Springer
Page : 84 pages
File Size : 46,9 Mb
Release : 2018-03-22
Category : Computers
ISBN : 9783319753041

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Deep Neural Networks in a Mathematical Framework by Anthony L. Caterini,Dong Eui Chang Pdf

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 : Jong Chul Ye
Publisher : Springer Nature
Page : 338 pages
File Size : 51,6 Mb
Release : 2022-01-05
Category : Mathematics
ISBN : 9789811660467

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Geometry of Deep Learning by Jong Chul Ye Pdf

The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.

Author : Lawrence J. Landau
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781447134275

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Concepts for Neural Networks by Lawrence J. Landau Pdf

Concepts for Neural Networks - A Survey provides a wide-ranging survey of concepts relating to the study of neural networks. It includes chapters explaining the basics of both artificial neural networks and the mathematics of neural networks, as well as chapters covering the more philosophical background to the topic and consciousness. There is also significant emphasis on the practical use of the techniques described in the area of robotics. Containing contributions from some of the world's leading specialists in their fields (including Dr. Ton Coolen and Professor Igor Aleksander), this volume will provide the reader with a good, general introduction to the basic concepts needed to understan d and use neural network technology.

Author : Ronald T. Kneusel
Publisher : No Starch Press
Page : 346 pages
File Size : 44,6 Mb
Release : 2021-11-23
Category : Computers
ISBN : 9781718501911

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Math for Deep Learning by Ronald T. Kneusel Pdf

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.

Author : Marcel Danesi
Publisher : Springer Nature
Page : 344 pages
File Size : 47,8 Mb
Release : 2019-09-14
Category : Mathematics
ISBN : 9783030225377

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Interdisciplinary Perspectives on Math Cognition by Marcel Danesi Pdf

This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.

Author : Jay Dawani
Publisher : Packt Publishing Ltd
Page : 347 pages
File Size : 54,5 Mb
Release : 2020-06-12
Category : Computers
ISBN : 9781838641849

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Hands-On Mathematics for Deep Learning by Jay Dawani Pdf

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.

Author : Kevin Gurney
Publisher : CRC Press
Page : 234 pages
File Size : 40,5 Mb
Release : 2018-10-08
Category : Computers
ISBN : 9781482286991

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An Introduction to Neural Networks by Kevin Gurney Pdf

Though mathematical ideas underpin the study of neural networks, the author presents the fundamentals without the full mathematical apparatus. All aspects of the field are tackled, including artificial neurons as models of their real counterparts; the geometry of network action in pattern space; gradient descent methods, including back-propagation; associative memory and Hopfield nets; and self-organization and feature maps. The traditionally difficult topic of adaptive resonance theory is clarified within a hierarchical description of its operation. The book also includes several real-world examples to provide a concrete focus. This should enhance its appeal to those involved in the design, construction and management of networks in commercial environments and who wish to improve their understanding of network simulator packages. As a comprehensive and highly accessible introduction to one of the most important topics in cognitive and computer science, this volume should interest a wide range of readers, both students and professionals, in cognitive science, psychology, computer science and electrical engineering.

Author : David Vernon
Publisher : MIT Press
Page : 284 pages
File Size : 51,9 Mb
Release : 2014-10-17
Category : Science
ISBN : 9780262028387

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Artificial Cognitive Systems by David Vernon Pdf

A concise introduction to a complex field, bringing together recent work in cognitive science and cognitive robotics to offer a solid grounding on key issues. This book offers a concise and accessible introduction to the emerging field of artificial cognitive systems. Cognition, both natural and artificial, is about anticipating the need for action and developing the capacity to predict the outcome of those actions. Drawing on artificial intelligence, developmental psychology, and cognitive neuroscience, the field of artificial cognitive systems has as its ultimate goal the creation of computer-based systems that can interact with humans and serve society in a variety of ways. This primer brings together recent work in cognitive science and cognitive robotics to offer readers a solid grounding on key issues. The book first develops a working definition of cognitive systems—broad enough to encompass multiple views of the subject and deep enough to help in the formulation of theories and models. It surveys the cognitivist, emergent, and hybrid paradigms of cognitive science and discusses cognitive architectures derived from them. It then turns to the key issues, with chapters devoted to autonomy, embodiment, learning and development, memory and prospection, knowledge and representation, and social cognition. Ideas are introduced in an intuitive, natural order, with an emphasis on the relationships among ideas and building to an overview of the field. The main text is straightforward and succinct; sidenotes drill deeper on specific topics and provide contextual links to further reading.

Author : Michael Taylor
Publisher : Independently Published
Page : 168 pages
File Size : 51,7 Mb
Release : 2017-10-04
Category : Computers
ISBN : 1549893645

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The Math of Neural Networks by Michael Taylor Pdf

There are many reasons why neural networks fascinate us and have captivated headlines in recent years. They make web searches better, organize photos, and are even used in speech translation. Heck, they can even generate encryption. At the same time, they are also mysterious and mind-bending: how exactly do they accomplish these things ? What goes on inside a neural network?On a high level, a network learns just like we do, through trial and error. This is true regardless if the network is supervised, unsupervised, or semi-supervised. Once we dig a bit deeper though, we discover that a handful of mathematical functions play a major role in the trial and error process. It also becomes clear that a grasp of the underlying mathematics helps clarify how a network learns. In the following chapters we will unpack the mathematics that drive a neural network. To do this, we will use a feedforward network as our model and follow input as it moves through the network.

Author : Ovidiu Calin
Publisher : Springer Nature
Page : 760 pages
File Size : 42,9 Mb
Release : 2020-02-13
Category : Mathematics
ISBN : 9783030367213

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Deep Learning Architectures by Ovidiu Calin Pdf

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.