Neural Networks and Qualitative Physics: A Viability Approach

Neural Networks and Qualitative Physics: A Viability Approach

by Jean-Pierre Aubin
     
 

ISBN-10: 1107402840

ISBN-13: 9781107402843

Pub. Date: 08/11/2011

Publisher: Cambridge University Press

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…  See more details below

Overview

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:
9781107402843
Publisher:
Cambridge University Press
Publication date:
08/11/2011
Edition description:
Reissue
Pages:
302
Product dimensions:
6.00(w) x 8.90(h) x 0.70(d)

Table of Contents

Preface
Acknowledgements
1Neural Networks: A Control Approach1
2Pseudoinverses and Tensor Products23
3Associative Memories44
4The Gradient Method61
5Nonlinear Neural Networks75
6External Learning Algorithm for Feedback Controls100
7Internal Learning Algorithm for Feedback Controls118
8Learning Processes of Cognitive Systems139
9Qualitative Analysis of Static Problems160
10Dynamical Qualitative Simulation187
Appendix 1: Convex and Nonsmooth Analysis219
Appendix 2: Control of an AUV252
Bibliography262
Index280

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