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Synopsis
This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics.
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Book Description
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, and set-valued analysis that plays a crucial role in qualitative analysis and simulation.
Synopsis
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 left several mathematical questions unanswered 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-values 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. 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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Neural Networks and Qualitative Physics : A Viability Approach
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Cambridge University Press, 1996
ISBN 10: 0521445329
ISBN 13: 9780521445320
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Neural Networks and Qualitative Physics : A Viability Approach
Published by
Cambridge University Press, 1996
ISBN 10: 0521445329
ISBN 13: 9780521445320
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Neural Networks and Qualitative Physics
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ISBN 13: 9780521445320
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