A spherical Hopfield model
| Autor: | Toni Verbeiren, Désiré Bollé, Th. M. Nieuwenhuizen, I Pérez Castillo |
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| Přispěvatelé: | Quantum Condensed Matter Theory (ITFA, IoP, FNWI) |
| Rok vydání: | 2003 |
| Předmět: |
Physics
Statistical Mechanics (cond-mat.stat-mech) Quantitative Biology::Neurons and Cognition Artificial neural network Closed set Replica FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Quantitative Biology Continuous variable symbols.namesake FOS: Biological sciences Quartic function symbols Statistical physics Hamiltonian (quantum mechanics) Langevin dynamics Quantitative Biology (q-bio) Condensed Matter - Statistical Mechanics Mathematical Physics |
| Zdroj: | Journal of Physics. A, Mathematical and General, 36, 10269-10277. IOP Publishing Ltd. |
| ISSN: | 1361-6447 0305-4470 |
| Popis: | We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equations for the order parameters and effective correlation and response function typical for neural networks. The stationary limit corresponds to the thermodynamic results. Numerical calculations illustrate our findings. 9 pages Latex including 3 eps figures, Addition of an author in the HTML-abstract unintentionally forgotten, no changes to the manuscript |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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