Mathematical Perspectives on Neural Networks

Abstract

Contents: Preface: Multilayer Structure of the Book and Its Summaries. P. Smolensky, Overview: Computational, Dynamical, and Statistical Perspectives on the Processing and Learning Problems in Neural Network Theory. Part I: Computational Perspectives. P. Smolensky, Overview: Computational Perspectives on Neural Networks. S. Franklin, M. Garzon, Computation by Discrete Neural Nets. I. Parberry, Circuit Complexity and Feedforward Neural Networks. J.S. Judd, Complexity of Learning. E.H.L Aarts, J.H.M. Korst, P.J. Zwietering, Deterministic and Randomized Local Search. M.B. Pour-El, The Mathematical Theory of the Analog Computer. Part II: Dynamical Perspectives. P. Smolensky, Overview: Dynamical Perspectives on Neural Networks. M.W. Hirsch, Dynamical Systems. L.F. Abbott, Statistical Analysis of Neural Networks. K.S. Narendra, S-M. Li, Neural Networks in Control Systems. A.S. Weigend, Time Series Analysis and Prediction. Part III: Statistical Perspectives. P. Smolensky, Overview: Statistical Perspectives on Neural Networks. R. Szeliski, Regularization in Neural Nets. D.E. Rumelhart, R. Durbin, R. Goldin, Y. Chauvin, Backpropagation: The Basic Theory. J. Rissanen, Information Theory and Neural Nets. A. Nadas, R.L. Mercer, Hidden Markov Models and Some Connections with Artificial Neural Nets. D. Haussler, Probably Approximately Correct Learning and Decision-Theoretic Generalizations. H. White, Parametric Statistical Estimation with Artificial Neural Networks. V.N. Vapnik, Inductive Principles of Statistics and Learning Theory.