Categorization in the symmetrically dilute hopfield network

• Autor(a) principal: Krebs, Paulo Roberto
• Data de Publicação: 1999
• Outros Autores: Theumann, Walter Karl
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRGS
• Texto Completo: http://hdl.handle.net/10183/103711
• topic: Redes neurais de hopfield; Diagramas de fase

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.