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Theoretical Advances in Neural Computation and Learning brings together in one volume some of the recent advances in the development of a theoretical framework for studying neural networks. A variety of novel techniques from disciplines such as computer science, electrical engineering, statistics, and mathematics have been integrated and applied to develop ground-breaking analytical tools for such studies. This volume emphasizes the computational issues in artificial neural networks and compiles a set of pioneering research works, which together establish a general framework for studying the complexity of neural networks and their learning capabilities. This book represents one of the first efforts to highlight these fundamental results, and provides a unified platform for a theoretical exploration of neural computation. Each chapter is authored by a leading researcher and/or scholar who has made significant contributions in this area.
Part 1 provides a complexity theoretic study of different models of neural computation. Complexity measures for neural models are introduced, and techniques for the efficient design of networks for performing basic computations, as well as analytical tools for understanding the capabilities and limitations of neural computation are discussed. The results describe how the computational cost of a neural network increases with the problem size. Equally important, these results go beyond the study of single neural elements, and establish to computational power of multilayer networks.
Part 2 discusses concepts and results concerning learning using models of neural computation. Basic concepts such as VC-dimension and PAC-learning are introduced, and recent results relating neural networks to learning theory are derived. In addition, a number of the chapters address fundamental issues concerning learning algorithms, such as accuracy and rate of convergence, selection of training data, and efficient algorithms for learning useful classes of mappings.
Foreword; B. Widrow. Foreword; D.E. Rummelhart. Preface. Part I: Computational Complexity of Neural Networks. 1. Neural Models and Spectral Methods; V. Roychowdhury, Kai-Yeung Siu, A. Orlitsky. 2. Depth-Efficient Threshold Circuits for Arithmetic Functions; T. Hofmeister. 3. Communication Complexity and Lower Bounds for Threshold Circuits; M. Goldmann. 4. A Comparison of the Computational Power of Sigmoid and Boolean Threshold Circuits; W. Maass, G. Schnitger, E.D. Sontag. 5. Computing on Analog Neural Nets with Arbitrary Real Weights; W. Maass. 6. Connectivity versus Capacity in the Hebb Rule; S.S. Venkatesh. Part II: Learning and Neural Networks. 7. Computational Learning Theory and Neural Networks: a Survey of Selected Topics; G. Turán. 8. Perspectives of Current Research about the Complexity of Learning on Neural Nets; W. Maass. 9. Learning an Intersection of K Halfspaces over a Uniform Distribution; A.L. Blum, R. Kannan. 10. On the Intractability of Loading Neural Networks; B. DasGupta, H.T. Siegelmann, E. Sontag. 11. Learning Boolean Functions via the Fourier Transform; Y. Mansour. 12. LMS and Backpropagation are Minimax Filters; B. Hassibi, A.H. Sayed, T. Kailath. 13. Supervised Learning: Can it Escape its Local Minimum? P.J. Werbos. Index.