Mathematical Perspectives on Neural Networks

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Author :
Publisher : Psychology Press
ISBN 13 : 1134773013
Total Pages : 890 pages
Book Rating : 4.1/5 (347 download)

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Book Synopsis Mathematical Perspectives on Neural Networks by : Paul Smolensky

Download or read book Mathematical Perspectives on Neural Networks written by Paul Smolensky and published by Psychology Press. This book was released on 2013-05-13 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Perspectives on Neural Networks

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Author :
Publisher :
ISBN 13 : 9780805812022
Total Pages : 900 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Mathematical Perspectives on Neural Networks by : Paul Smolensky

Download or read book Mathematical Perspectives on Neural Networks written by Paul Smolensky and published by . This book was released on 1996-05 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hands-On Mathematics for Deep Learning

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Publisher : Packt Publishing Ltd
ISBN 13 : 183864184X
Total Pages : 347 pages
Book Rating : 4.8/5 (386 download)

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Book Synopsis Hands-On Mathematics for Deep Learning by : Jay Dawani

Download or read book Hands-On Mathematics for Deep Learning written by Jay Dawani and published by Packt Publishing Ltd. This book was released on 2020-06-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Methods for Neural Network Analysis and Design

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Author :
Publisher : MIT Press
ISBN 13 : 9780262071741
Total Pages : 452 pages
Book Rating : 4.0/5 (717 download)

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Book Synopsis Mathematical Methods for Neural Network Analysis and Design by : Richard M. Golden

Download or read book Mathematical Methods for Neural Network Analysis and Design written by Richard M. Golden and published by MIT Press. This book was released on 1996 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.

Discrete Mathematics of Neural Networks

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Author :
Publisher : SIAM
ISBN 13 : 089871480X
Total Pages : 137 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Discrete Mathematics of Neural Networks by : Martin Anthony

Download or read book Discrete Mathematics of Neural Networks written by Martin Anthony and published by SIAM. This book was released on 2001-01-01 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of Deep Learning

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Author :
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111025802
Total Pages : 666 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Mathematics of Deep Learning by : Leonid Berlyand

Download or read book Mathematics of Deep Learning written by Leonid Berlyand and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-04-27 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Math for Deep Learning

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Author :
Publisher : No Starch Press
ISBN 13 : 1718501919
Total Pages : 346 pages
Book Rating : 4.7/5 (185 download)

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Book Synopsis Math for Deep Learning by : Ronald T. Kneusel

Download or read book Math for Deep Learning written by Ronald T. Kneusel and published by No Starch Press. This book was released on 2021-11-23 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Deep Learning

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Author :
Publisher : Springer Nature
ISBN 13 : 9811660468
Total Pages : 338 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Geometry of Deep Learning by : Jong Chul Ye

Download or read book Geometry of Deep Learning written by Jong Chul Ye and published by Springer Nature. This book was released on 2022-01-05 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Math and Architectures of Deep Learning

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Author :
Publisher : Simon and Schuster
ISBN 13 : 1617296481
Total Pages : 550 pages
Book Rating : 4.6/5 (172 download)

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Book Synopsis Math and Architectures of Deep Learning by : Krishnendu Chaudhury

Download or read book Math and Architectures of Deep Learning written by Krishnendu Chaudhury and published by Simon and Schuster. This book was released on 2024-03-26 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of Neural Networks

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461560993
Total Pages : 423 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Mathematics of Neural Networks by : Stephen W. Ellacott

Download or read book Mathematics of Neural Networks written by Stephen W. Ellacott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Deep Learning Architectures

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Publisher : Springer Nature
ISBN 13 : 3030367215
Total Pages : 760 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Deep Learning Architectures by : Ovidiu Calin

Download or read book Deep Learning Architectures written by Ovidiu Calin and published by Springer Nature. This book was released on 2020-02-13 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Deep Neural Networks in a Mathematical Framework

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Author :
Publisher : Springer
ISBN 13 : 3319753045
Total Pages : 95 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Deep Neural Networks in a Mathematical Framework by : Anthony L. Caterini

Download or read book Deep Neural Networks in a Mathematical Framework written by Anthony L. Caterini and published by Springer. This book was released on 2018-03-22 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics for Machine Learning

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Publisher : Cambridge University Press
ISBN 13 : 1108569323
Total Pages : 392 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Math and Architectures of Deep Learning

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Author :
Publisher : Simon and Schuster
ISBN 13 : 1638350809
Total Pages : 550 pages
Book Rating : 4.6/5 (383 download)

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Book Synopsis Math and Architectures of Deep Learning by : Krishnendu Chaudhury

Download or read book Math and Architectures of Deep Learning written by Krishnendu Chaudhury and published by Simon and Schuster. This book was released on 2024-05-21 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shine a spotlight into the deep learning “black box”. This comprehensive and detailed guide reveals the mathematical and architectural concepts behind deep learning models, so you can customize, maintain, and explain them more effectively. Inside Math and Architectures of Deep Learning you will find: Math, theory, and programming principles side by side Linear algebra, vector calculus and multivariate statistics for deep learning The structure of neural networks Implementing deep learning architectures with Python and PyTorch Troubleshooting underperforming models Working code samples in downloadable Jupyter notebooks The mathematical paradigms behind deep learning models typically begin as hard-to-read academic papers that leave engineers in the dark about how those models actually function. 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. Written by deep learning expert Krishnendu Chaudhury, 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. Foreword by Prith Banerjee. About the technology Discover what’s going on inside the black box! To work with deep learning you’ll have to choose the right model, train it, preprocess your data, evaluate performance and accuracy, and deal with uncertainty and variability in the outputs of a deployed solution. This book takes you systematically through the core mathematical concepts you’ll need as a working data scientist: vector calculus, linear algebra, and Bayesian inference, all from a deep learning perspective. About the book Math and Architectures of Deep Learning teaches the math, theory, and programming principles of deep learning models laid out side by side, and then puts them into practice with well-annotated Python code. You’ll progress from algebra, calculus, and statistics all the way to state-of-the-art DL architectures taken from the latest research. What's inside The core design principles of neural networks Implementing deep learning with Python and PyTorch Regularizing and optimizing underperforming models About the reader Readers need to know Python and the basics of algebra and calculus. About the author Krishnendu Chaudhury is co-founder and CTO of the AI startup Drishti Technologies. He previously spent a decade each at Google and Adobe. Table of Contents 1 An overview of machine learning and deep learning 2 Vectors, matrices, and tensors in machine learning 3 Classifiers and vector calculus 4 Linear algebraic tools in machine learning 5 Probability distributions in machine learning 6 Bayesian tools for machine learning 7 Function approximation: How neural networks model the world 8 Training neural networks: Forward propagation and backpropagation 9 Loss, optimization, and regularization 10 Convolutions in neural networks 11 Neural networks for image classification and object detection 12 Manifolds, homeomorphism, and neural networks 13 Fully Bayes model parameter estimation 14 Latent space and generative modeling, autoencoders, and variational autoencoders A Appendix

Introduction To The Theory Of Neural Computation

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Author :
Publisher : CRC Press
ISBN 13 : 0429968213
Total Pages : 352 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Introduction To The Theory Of Neural Computation by : John A. Hertz

Download or read book Introduction To The Theory Of Neural Computation written by John A. Hertz and published by CRC Press. This book was released on 2018-03-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to the neural network models currently under intensive study for computational applications. It also provides coverage of neural network applications in a variety of problems of both theoretical and practical interest.

The Principles of Deep Learning Theory

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Author :
Publisher : Cambridge University Press
ISBN 13 : 1316519333
Total Pages : 473 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis The Principles of Deep Learning Theory by : Daniel A. Roberts

Download or read book The Principles of Deep Learning Theory written by Daniel A. Roberts and published by Cambridge University Press. This book was released on 2022-05-26 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops an effective theory approach to understanding deep neural networks of practical relevance.

Concepts for Neural Networks

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1447134273
Total Pages : 316 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Concepts for Neural Networks by : Lawrence J. Landau

Download or read book Concepts for Neural Networks written by Lawrence J. Landau and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.