Taylor J.G. (ed.) Mathematical Approaches to Neural Networks

Издательство North-Holland, 1993, -391 pp.The subject of Neural Networks is being seen to be coming of age, after its initial inception 50 years ago in the seminal work of McCulloch and Pitts. A distinguished gallery of workers (some of whom are included in this volume) have contributed to building the edifice which is now proving of value in a wide range of academic disciplines and in important applications in industrial and business tasks. These two strands of neural networks are thus firstly appertaining to living systems, their explanation and modelling, and secondly that to dedicated tasks to which living systems may be ill adapted or involve uncertain rules in noisy environments, the progress being made in both these approaches is considerable, but yet both stand in need of a theoretical framework of explanation underpinning their usage and allowing the progress being made to be put on a firmer footing. The purpose of this book is to attempt to provide such a framework.
Mathematics is rightly to be regarded as the queen of the sciences, and it is through mathematical approaches to neural networks that a suitable explanatory framework is expected to be found. Various approaches are available here, and are contained in the contributions presented here. These span a broad range from single neuron details, through to numerical analysis, functional analysis and dynamical systems theory. Each of these avenues provides its own insights into the way neural networks can be understood, both for artificial ones through to simplified simulations. The breath and vigour of the contributions underline the importance of the ever-deepening mathematical understanding of neural networks.Control Theory Approach
Computational Learning Theory for Artificial Neural Networks
Time-sum mating Network Approach
The Numerical Analysis Approach
Self-organising Neural Networks for Stable Control of Autonomous Behavior in a Changing World
On-line Learning Processes in Artificial Neural Networks
Multilayer Functionals
Neural Networks: The Spin Glass Approach
Dynamics of Attractor Neural Networks
Information Theory and Neural Networks
Mathematical Analysis of a Competitive Network for Attention