Neural Networks and Qualitative Physics

Download or read book Neural Networks and Qualitative Physics written by Jean-Pierre Aubin and published by Cambridge University Press. This book was released on 1996-03-29 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.