Rl. Costa et A. Theumann, Categorization in a Hopfield network trained with weighted examples. (I). Finite number of concepts, PHYSICA A, 268(3-4), 1999, pp. 499-512
We consider the categorization problem in a Hopfield network with a finite
number of concepts and trained with s examples of weight lambda(tau), tau =
1,...,s. We find that the retrieval capacity of an example with weight lam
bda(1), and the corresponding categorization error, depends also on the ari
thmetic mean lambda(m) = (1/(s - 1)) Sigma(tau=2)(s) lambda(tau) of the oth
er weights. For lambda(1)/lambda(m) < 1, the categorization process is simi
lar to that in a network trained with Hebb's rule, but for lambda(1)/lambda
(m) >1 we find that the line of first-order transitions between the retriev
al and categorization phases ends at a critical point in the s, T plane. Wh
en two solutions are present, the global minimum of the free energy corresp
onds to the solution with the highest weight. (C) 1999 Elsevier Science B.V
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