Neural Networks and Qualitative Physics
A Viability Approach

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics.

Jean-Pierre Aubin (Author)

9781107402843, Cambridge University Press

Paperback / softback, published 11 August 2011

302 pages
22.9 x 15.2 x 1.6 cm, 0.41 kg

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.

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 simulation.

Subject Areas: Artificial intelligence [UYQ], Probability & statistics [PBT]