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9781107402843

Neural Networks and Qualitative Physics

by
  • ISBN13:

    9781107402843

  • ISBN10:

    1107402840

  • Edition: Revised
  • Format: Paperback
  • Copyright: 2011-08-11
  • Publisher: Cambridge Univ Pr

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Summary

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.

Table of Contents

Neural networks: a control approach
Pseudo-inverses and tensor products
Associative memories
The gradient method
Nonlinear neural networks
External learning algorithm of feedback controls
Internal learning algorithm of feedback controls
Learning processes of cognitive systems
Qualitative analysis of static problems
Dynamical qualitative simulation
Table of Contents provided by Publisher. All Rights Reserved.

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