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Discrete Mathematics of Neural Networks: Selected TopicsDiscrete Mathematics of Neural Networks: Selected Topics

Martin Anthony

SIAM Monographs on Discrete Mathematics and Applications 8

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.

The author discusses interesting connections between special types of Boolean functions and the simplest types of neural networks. 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.


This book is aimed primarily at graduate students and researchers in discrete mathematics. Readers need only a basic knowledge of discrete mathematics and probability theory to enjoy this book; no prior knowledge of neural networks is necessary.


Preface; Chapter 1: Artificial Neural Networks; Chapter 2: Boolean Functions; Chapter 3: Threshold Functions; Chapter 4: Number of Threshold Functions; Chapter 5: Sizes of Weights for Threshold Functions; Chapter 6: Threshold Order; Chapter 7: Threshold Networks and Boolean Functions; Chapter 8: Specifying Sets; Chapter 9: Neural Network Learning; Chapter 10: Probabilistic Learning; Chapter 11: VC-Dimensions of Neural Networks; Chapter 12: The Complexity of Learning; Chapter 13: Boltzmann Machines and Combinatorial Optimization; Bibliography; Index.

2001 / xii + 131 pages / Hardcover / ISBN-13: 978-0-898714-80-7 / ISBN-10: 0-89871-480-X /
List Price $78.50 / SIAM Member Price $54.95 / Order Code DT08
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