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. Catego...
| Veröffentlicht in: | Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. - 1993. - 60(1999), 4 Pt B vom: 30. Okt., Seite 4580-7 |
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| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1999
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| Zugriff auf das übergeordnete Werk: | Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | 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 |
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| Beschreibung: | Date Completed 16.07.2002 Date Revised 28.07.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1063-651X |