Capacities of multiconnected memory models

2014 We study generalizations of the Hopfield model for associative memory which contain interactions of R spins with one another and allow for different weights for input patterns. Using probabilistic considerations we show that stability criteria lead to capacities which increase like powers of NR-1. Investigating numerically the basins of attraction we find behaviour which agrees with theoretical expectations. We introduce the more stringent definition of « coverage-capacity » by requiring the whole phase-space to be covered by the basins of attraction of the input patterns. Even under these conditions we find large numbers of patterns which can be used to design an output spectrum by varying the input weights. J. Phys. France 49 (1988) 389-395 MARS 1988, Classification Physics Abstracts 05.50 75.10H 87.30G