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Categorization in the symmetrically dilute hopfield network

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Categorization in the symmetrically dilute hopfield network

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Título Categorization in the symmetrically dilute hopfield network
Autor Krebs, Paulo Roberto
Theumann, Walter Karl
Abstract 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.
Contido em Physical Review. E, Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics. New York. Vol. 60, no. 4, pt. B (Oct. 1999), p. 4580-4587
Assunto Diagramas de fase
Redes neurais de hopfield
Origem Estrangeiro
Tipo Artigo de periódico
URI http://hdl.handle.net/10183/103711
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