Mathematical Methods for Neural Network Analysis and Design (MIT Press)

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9780262071741: Mathematical Methods for Neural Network Analysis and Design (MIT Press)

This graduate-level text teaches students how to use a small number of powerful mathematical tools for analyzing and designing a wide variety of artificial neural network (ANN) systems, including their own customized neural networks.Mathematical Methods for Neural Network Analysis and Design offers an original, broad, and integrated approach that explains each tool in a manner that is independent of specific ANN systems. Although most of the methods presented are familiar, their systematic application to neural networks is new. Included are helpful chapter summaries and detailed solutions to over 100 ANN system analysis and design problems. For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.This text is unique in several ways. It is organized according to categories of mathematical tools -- for investigating the behavior of an ANN system, for comparing (and improving) the efficiency of system computations, and for evaluating its computational goals -- that correspond respectively to David Marr's implementational, algorithmic, and computational levels of description. And instead of devoting separate chapters to different types of ANN systems, it analyzes the same group of ANN systems from the perspective of different mathematical methodologies.A Bradford Book

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About the Author:

Richard M. Golden is Associate Professor, Cognition and Neuroscience Program, the University of Texas at Dallas. In addition, he is an independent engineering consultant specializing in the development of customized artificial neural networks and statistical analyses, and is a member of the editorial board of the journal Neural Networks.

Review:

The use of Marr's theory of complex information processing systems as the guideline for this text, rather than one of the more field-oriented approaches commonly found in the literature, offers a more diverse perspective. The idea of analysis of the implementation, algorithmic and computational levels of ANNs with the theory of dynamic systems, optimization and statistics provides fruitful insights. Furthermore the organization of the book allows students with the background in any one of these fields to use their knowledge successfully to get up to speed on the current issues of design. Overall, Golden's text offers access to a vast set of interesting issues using the tool that they have in common, bridging a gap in a literature consisting mainly of field specific technical treatments.

(Andreas Gottschling, University of California)

This is an excellent text and reference work that integrates diverse approaches in the artificial neural network field, and relates them to relevant fundamental mathematical work in areas such as nonlinear systems theory and optimization. The book will be very valuable for students and researchers who already have a basic understanding of the theory and programming of artificial neural networks.

(A. A. J. Marley, Professor and Chair, Department of Psychology, McGill University)

"A significant and scholarly contribution to the field of neural networks.The author successfully integrates a very broad range of material in acompetent and understandable manner. I do not know of any book on this sametopic that covers such a wide range of material." Jerome R. Busemeyer, Professor of Psychology, Purdue University

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