Mathematical Methods for Neural Network Analysis and Design

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MIT Press, 1996 - Computers - 419 pages
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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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Contents

Introduction
1
IMPLEMENTATIONAL LEVEL
65
Deterministic Nonlinear Dynamical Systems Analysis
115
Stochastic Nonlinear Dynamical Systems Analysis
151
Nonlinear Optimization Theory
193
Rational Inference Measures
241
Statistical Model Evaluation
313
Epilogue
351
References
387
Author Index
405
Subject Index
411
Copyright

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Page 389 - Cowey, A. (1981). Why are there so many visual areas? In FO Schmitt, FG Worden, G. Adelman and SG Dennis (Eds), The Organisation of the Cerebral Cortex.
Page 387 - Amari, S. ( 1977). Neural theory of association and concept-formation.
Page 387 - T. and Sveen, O. (1969). Participation of inhibitory and excitatory interneurons in the control of hippocampal cortical output. In The Interneuron (MAB Brazier, Ed.), pp.
Page 401 - In RP Lippmann, JE Moody and DS Touretzky (eds.), Advances in Neural Information Processing Systems 3, pp.

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About the author (1996)

Richard M. Golden is professor of history and Director of the Jewish Studies Program at the University of North Texas. He is author of The Godly Rebellion: Parisian Cures and the Religious Fronde, 1652-1662 (1981); editor of The Huguenot Connection: The Edict of Nantes, Its Revocation, and Early French Migration to South Carolina (1988); and editor of Church, State, and Society under the Bourbon Kings of France (1982). He coedited, with Thomas Kuehn, Western Societies: Primary Sources in Social History (1993). He is currently editing the Encyclopedia of Witchcraft: The Western Tradition, to be published in 2003.

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