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Discrete neural computation
Siu K. (ed), Roychowdhury V., Kailath T., Prentice-Hall, Inc., Upper Saddle River, NJ, 1995. Type: Book (9780133007084)
Date Reviewed: Jan 1 1996

In the past decade, there has been growing interest in neural networks and their applications in such disciplines as neurobiology, computer science, engineering, mathematics, and physics. This book brings together recent developments in discrete neural computation. The purpose of the book is “to integrate a variety of important ideas and analytical techniques and establish a theoretical foundation for discrete computation.” The authors rely on two principal models to present their ideas: threshold circuits and discrete-time  Hopfield  networks. A threshold circuit is a directed acyclic graph (a feedforward network) in which the output at each node is determined by a linear threshold function (a binary function that depends on a linear combination of weighted inputs and a threshold value). A discrete-time Hopfield network differs from a threshold network in that it allows feedback, and the state of each node is a function of discrete time. These two models are used to discuss the following central issues: comparison of neural network models with conventional models, neural network design procedures, and computational limitations. A recurring theme in this book is the demonstration that threshold circuits are more powerful computational models than conventional AND-OR circuits.

Although the reader needs some knowledge of Boolean algebra, linear algebra, probability theory, and computational complexity, chapter 1 provides the basics about neural computation and the discrete models that are needed for the rest of the book. Chapter 2 introduces the linear threshold element and discusses perceptron learning and linear nonseparability. Chapters 3 and 4 examine the design and analysis of threshold circuits used for common computations involving symmetric, arithmetic, and comparison functions. Various optimization issues that arise in the design of threshold circuits are dealt with in chapter 5. Chapter 6 analyzes issues related to the weights in threshold circuits. Chapter 7 addresses the issue of establishing lower bounds on the size of certain threshold circuits. Chapter 8 establishes some key lower bound results in threshold circuit complexity. Chapter9 demonstrates the limitations of constant-depth polynomial-size AND-OR circuits, and chapter 10 addresses complexity issues in unrestricted depth circuits. Finally, discrete Hopfield networks are discussed in chapter 11: the basic properties are derived, sequential machine characteristics involving transient and stable states are developed, and some applications are presented.

This book is a significant contribution to the study of neural networks and will be invaluable to researchers in discrete neural computation. The material is well organized and edited. The book has an extensive bibliography and an excellent exercise set, and it would be a fitting text for a graduate course in this area.

Reviewer:  Thomas B. Hilburn Review #: CR119316 (9601-0016)
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Self-Modifying Machines (F.1.1 ... )
 
 
Complexity Measures And Classes (F.1.3 )
 
 
General (F.2.0 )
 
 
General (B.7.0 )
 
 
Miscellaneous (B.6.m )
 
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