Neural Networks and Qualitative Physics: A Viability Approach

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This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. The rapid advances in these two areas have left unanswered several mathematical questions that should motivate and challenge mathematicians. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning algorithm" of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints. Mathematical models involve many features of a problem that may not be relevant to its solution. Qualitative physics, however, deals with an imperfect knowledge of the problem model. It is therefore more suited to the study of expert systems, which are shallow models and do not require structural knowledge of the problem. This book should be a valuable introduction to the field for researchers in neural networks and cognitive systems, and should help to expand the range of study for viability theorists.
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Product Details

  • ISBN-13: 9780521445320
  • Publisher: Cambridge University Press
  • Publication date: 3/28/1996
  • Pages: 301
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.75 (d)

Table of Contents

1 Neural Networks: A Control Approach 1
2 Pseudoinverses and Tensor Products 23
3 Associative Memories 44
4 The Gradient Method 61
5 Nonlinear Neural Networks 75
6 External Learning Algorithm for Feedback Controls 100
7 Internal Learning Algorithm for Feedback Controls 118
8 Learning Processes of Cognitive Systems 139
9 Qualitative Analysis of Static Problems 160
10 Dynamical Qualitative Simulation 187
Appendix 1: Convex and Nonsmooth Analysis 219
Appendix 2: Control of an AUV 252
Bibliography 262
Index 280
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