Discrete Mathematics of Neural Networks
Selected Topics

Considers key aspects of the burgeoning field of artificial neural network theory.

Martin Anthony (Author)

9780898714807, Society for Industrial and Applied Mathematics

Hardback, published 1 January 1987

143 pages
26.1 x 18.4 x 1.2 cm, 0.495 kg

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.

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.

Subject Areas: Neural networks & fuzzy systems [UYQN], Discrete mathematics [PBD]