Categorization in the symmetrically dilute Hopfield network.
A symmetrically dilute Hopfield model with a Hebbian learning rule is used to study the effects of gradual dilution and of synaptic noise on the categorization ability of an attractor neural network with hierarchically correlated patterns in a two-level structure of ancestors and descendants. Categorization consists in recognizing the ancestors when the network has been trained exclusively with the descendants. We consider a macroscopic number of ancestors, each with a finite number of descendants, and take into account the stochastic noise produced by the former in an equilibrium study of the network, by means of replica-symmetric mean-field theory. Phase diagrams are obtained that exhibit a categorization, a spin-glass, and a paramagnetic phase, as well as the dependence of the order parameters on the relevant quantities. The de Almeida-Thouless lines that limit the validity of the replica-symmetric results are also obtained. It is shown that gradual dilution increases considerably the region where a stable categorization phase may be found.
Krebs
P R
PR
Instituto de Física e Matemática, Universidade Federal de Pelotas, Caixa Postal 354, 96010-900 Pelotas, RS, Brazil.
Theumann
W K
WK
D055592:Biophysical Phenomena; D001703:Biophysics; D015233:Models, Statistical; D016011:Normal Distribution; D013269:Stochastic Processes; D013696:Temperature