Rl. Costa et A. Theumann, Categorization in a Hopfield network trained with weighted examples: Extensive number of concepts, PHYS REV E, 61(5), 2000, pp. 4860-4865
We consider the categorization problem in a Hopfield network with an extens
ive number of concepts p = alpha N and trained with s examples of weight la
mbda(tau) tau=1,...,s in the presence of synaptic noise represented by a di
mensionless "temperature" T. We find that the retrieval capacity of an exam
ple with weight lambda(l), and the corresponding categorization error, depe
nd also on the arithmetic mean lambda(m) of the other weights. The categori
zation process is similar to that in a network trained with Hebb's rule, bu
t for lambda(l)/lambda(m) > 1 the retrieval phase is enhanced. We present t
he phase diagram in the T-alpha plane, together with the de Almeida-Thoules
s line of instability. The phase diagrams in the alpha-s plane are discusse
d in the absence of synaptic noise and several values of the correlation pa
rameter b.