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Neural Networks and Qualitative Physics: A Viability Approach
     

Neural Networks and Qualitative Physics: A Viability Approach

by Jean-Pierre Aubin
 

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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. 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:
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

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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