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 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.