Issue
J. Phys. I France
Volume 7, Number 12, December 1997
Page(s) 1709 - 1721
DOI https://doi.org/10.1051/jp1:1997165
DOI: 10.1051/jp1:1997165
J. Phys. I France 7 (1997) 1709-1721

Storage Capacity of Generalized Palimpsests

D. Bonnaz

Institut de Physique Expérimentale, Université de Lausanne, 1015 Lausanne, Switzerland



(Received 24 April 1997, revised 11 June 1997, accepted 22 August 1997)

Abstract
A simple analytical study of a short term memory model is performed. This model consists of a symmetric p-neuron interaction between N neurons. Learning is achieved by a generalized Hebb rule. Saturation is prevented by the introduction of a bound A to the couplings. At each time step, an input pattern is drawn at random, independently of the previous ones. The determination of the life time T of a memorized pattern viewed as a function of A and N is accomplished by a statistical study of the dynamic of the learning process which has been made possible under the assumption that the couplings evolve independently. This simplification reduces the determination of T to a one-dimensional problem, by considering energies rather than couplings. The choice of the optimal value $A_{\rm opt}$ of A is a compromise between the success of the learning process and the maximization of T. The essential results are expressed by the formulae $T\propto A^2$ and $A_{\rm opt}\propto N^{\frac{p-1}{2}}$.



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