| Numéro |
J. Phys. I France
Volume 2, Numéro 3, March 1992
|
|
|---|---|---|
| Page(s) | 247 - 250 | |
| DOI | https://doi.org/10.1051/jp1:1992140 | |
J. Phys. I France 2 (1992) 247-250
Reetrant spin glass behaviour in the replica symmetric solution of the Hopfield neural network model
Jean-Pierre Naef and Andrew CanningDépartement de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
(Received 18 November 1991, accepted 6 December 1991)
Abstract
Numerical and analytical solutions at low temperature are presented for the replica symmetric order parameter equations of
the Hopfield neural model with interactions between all the spins. We find that these equations give weak reentrant spin glass
behaviour at
T<0.023. This is similar behaviour to that found for the replica symmetric solution of the SK spin glass [4] although in that case
the reentrant phase is much larger. It is also known from what is believed to be the true solution for the SK spin glass that
this reentrant behaviour is unphysical so, by analogy, we believe it is unphysical for neural network models. Even so, the
maximum value in replica theory of
, which measures the storage capacity of the Hopfield model, is to be found at
. This is slightly higher than the zero temperature value of
© Les Editions de Physique 1992