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Neural Networks and Qualitative Physics: A Viability Approach by Jean-Pierre Aubin

Neural Networks and Qualitative Physics: A Viability Approach

by Jean-Pierre Aubin
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Book cover type: Paperback
  • ISBN13: 9781107402843
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 302
  • Original Price: GBP 55.0
  • Language: English
  • Edition: Reissue
  • Item Weight: 404 grams
  • BISAC Subject(s): Mathematical Analysis

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.

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