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  3. Neural Networks and Qualitative Physics
  • Cited by 22
Publisher:
Cambridge University Press
Online publication date:
August 2012
Print publication year:
1996
Online ISBN:
9780511626258
DOI:
https://doi.org/10.1017/CBO9780511626258
Subjects:
Mathematics, Computational Science, Abstract Analysis
Information

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, 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. This book will be of value to anyone with an interest in neural networks and cognitive systems.

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