| Numéro |
J. Phys. I France
Volume 7, Numéro 12, December 1997
|
|
|---|---|---|
| Page(s) | 1709 - 1721 | |
| DOI | https://doi.org/10.1051/jp1:1997165 | |
J. Phys. I France 7 (1997) 1709-1721
Storage Capacity of Generalized Palimpsests
D. BonnazInstitut 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
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
and
.
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