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- catalog abstract ""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 have left unanswered several mathematical questions 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-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." "Mathematical models involve many features of a problem that may not be relevant to its solution. Qualitative physics, however, deals with an imperfect knowledge of the problem model. It is therefore more suited to the study of expert systems, which are shallow models and do not require structural knowledge of the problem." "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."--BOOK JACKET.".
- catalog alternative "Subtitle on cover: Viability approach".
- catalog contributor b9754606.
- catalog created "1996.".
- catalog date "1996".
- catalog date "1996.".
- catalog dateCopyrighted "1996.".
- catalog description ""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 have left unanswered several mathematical questions 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-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." "Mathematical models involve many features of a problem that may not be relevant to its solution. Qualitative physics, however, deals with an imperfect knowledge of the problem model. It is therefore more suited to the study of expert systems, which are shallow models and do not require structural knowledge of the problem." "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."--BOOK JACKET.".
- catalog description "Includes bibliographical references (p. 262-279) and index.".
- catalog description "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 -- Appendix A. Convex and nonsmooth analysis -- Appendix B. Control of an AUV.".
- catalog extent "xvii, 283 p. :".
- catalog identifier "0521445329 (hardback)".
- catalog issued "1996".
- catalog issued "1996.".
- catalog language "eng".
- catalog publisher "Cambridge ; New York : Cambridge University Press,".
- catalog subject "006.3 20".
- catalog subject "Artificial intelligence Mathematics.".
- catalog subject "Mathematical physics.".
- catalog subject "Neural networks (Computer science)".
- catalog subject "Q335 .A88 1996".
- catalog tableOfContents "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 -- Appendix A. Convex and nonsmooth analysis -- Appendix B. Control of an AUV.".
- catalog title "Neural networks and qualitative physics / Jean-Pierre Aubin.".
- catalog title "Subtitle on cover: Viability approach".
- catalog type "text".