Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

Preface: Multilayer Structure of the Book and Its Summaries

One of the delights of the field of neural or connectionist networks is the great diversity of perspectives from which these nets can be profitability studied. Biological and cognitive perspectives are important among these, but in this book we focus on mathematical perspectives, from which these networks appear as purely formal systems.

Throughout the history of the neural networks field, broadly construed, major turning points have been marked by developments of a primarily mathematical nature: consider how the field was changed forever by the work of McCulloch and Pitts, Rosenblatt, Minsky and Papert, Grossberg, Kohonen, Hopfield, the development of the Boltzmann and back-propagation learning algorithms, and many other equally important formal advances. Mathematical perspectives have been central to the field from its inception.

To say we are limiting ourselves in this book to mathematical perspectives is not at all to say that we are operating within narrow boundaries. For even the purely mathematical perspectives on neural networks constitute an extremely rich and diverse class: neural networks are collections of Boolean gates, collections of analog gates, evolving dynamical systems, stochastic processes, models of stochastic processes, function approximators, Bayesian probabilistic models, information-theoretic analyzers, statistical parameter estimators--just to sample the perspectives represented in this book alone.

The purpose of this book is to introduce to students of neural networks a wide variety of mathematical perspectives which contribute conceptual and technical insights into the power and limits of processing and learning in these networks.

-xiii-

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