J. Phys. I France
Volume 7, Number 12, December 1997
Page(s) 1709 - 1721
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)

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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