Neural Networks and Qualitative Physics: A Viability Approach

Neural Networks and Qualitative Physics: A Viability Approach

by Jean-Pierre Aubin, Jean-Pierre Aubin
     
 

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ISBN-10: 0521445329

ISBN-13: 9780521445320

Pub. Date: 03/28/1996

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. 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

Overview

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. 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.

Product Details

ISBN-13:
9780521445320
Publisher:
Cambridge University Press
Publication date:
03/28/1996
Pages:
301
Product dimensions:
5.98(w) x 8.98(h) x 0.75(d)

Table of Contents

1. Neural networks: a control approach; 2. Pseudo-inverses and tensor products; 3. Associative memories; 4. The gradient method; 5. Nonlinear neural networks; 6. External learning algorithm of feedback controls; 7. Internal learning algorithm of feedback controls; 8. Learning processes of cognitive systems; 9. Qualitative analysis of static problems; 10. Dynamical qualitative simulation.

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