Reverberations and control of neural networks

Summary The simulation of neural networks, such as the brain cortex, which have a diffuse and rather uniform structure quite unlike the simple block-structure of extant computers, leads naturally to the study of functions and principles which only in part fall within the scope of Automata Theory. Systems of decision equations must be studied with a view especially to obtaining practical means for the prevision and computation of diffuse reverberations of wanted general characteristics, with the exclusion of all others. This amounts to deriving constraints on the allowed variability of the couplings among elements during learning processes, failing which the behavior of the simulator would become uncontrollable for practical purposes. A simple mathematical treatment is presented, which essentially linearizes these problems by an appropriate use of matrix algebra and permits a straightforward study of the wanted conditions, as well as of the controlling elements which may have to be added to the network.This work has been performed in part at the Laboratoire de Physique Théorique et Hautes Energies, Faculté des Sciences de Paris.This work has been performed with the joint sponsorship of the U.S.A.F. and their European Office of Aerospace Research under contracts no. AF EOAR 66-25 and AF 33(615)-2786.We wish to express our sincere thanks to Dr. F. Lauria for many illuminated discussions; and to Prof. M. Lévy for his kind hospitality at the Laboratoire de physique Théorique, in Paris, where part of this research was made.