Neural Networks and Qualitative Physics A Viability Approach [Hardcover]

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics.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.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.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.1. Neural networks: a control approach; 2. Pseudo-inverses and tensor products; 3. Associative memories; 4. The gradient method; 5. Nonlinear neural networks; 6. External learning algorithm of feedback controls; 7. Internal learning algorithm of feedback controls; 8. Learning processes of cognitive systems; 9. Qualitative analysis of static problems; 10. Dynamical qualitative simulal&