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Discrete Mathematics of Neural Networks

Discrete Mathematics of Neural Networks
Selected Topics

Part of Monographs on Discrete Mathematics and Applications

  • Author: Martin Anthony, London School of Economics and Political Science
  • Date Published: April 2001
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898714807

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  • 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.

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    Product details

    • Date Published: April 2001
    • format: Hardback
    • isbn: 9780898714807
    • length: 143 pages
    • dimensions: 261 x 184 x 12 mm
    • weight: 0.495kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

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

  • Author

    Martin Anthony, London School of Economics and Political Science

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