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Título : | Associative Memory in a Continuous Metric Space: A Theoretical Foundation |
Otros títulos : | Memoria Asociativa en un Espacio M etrico Continuo: Fundamentos Te oricos |
Autor : | Carlos Segura, Enrique |
Palabras clave : | Keywords. associative memory, continuous metric space, dynamical systems, Hopfield model, stability, Glauber dynamics, continuous topology. |
Fecha de publicación : | 15-oct-2009 |
Editorial : | Revista Computación y Sistemas; Vol. 13 No. 2 |
Citación : | Revista Computación y Sistemas; Vol. 13 No. 2 |
Citación : | Revista Computación y Sistemas;Vol. 13 No. 2 |
Resumen : | Abstract We introduce a formal theoretical background, which includes theorems and their proofs, for a neural network model with associative memory and continuous topology, i.e. its processing units are elements of a continuous metric space and the state space is Euclidean and infinite dimensional. This approach is intended as a generalization of the previous ones due to Little and Hopfield. The main contribution of the present work is to integrate -and to provide a theoretical background that makes this integration consistent- two levels of continuity: i) continuous response processing units and ii) continuous topology of the neural system, obtaining a more biologically plausible model of associative memory. We present our analysis according to the following sequence of steps: general results concerning attractors and stationary solutions, including a variational approach for the derivation of the energy function; focus on the case of orthogonal memories, proving theorems on stability, size of attraction basins and spurious states; considerations on the problem of resolution, analyzing the more general case of memories that are not orthogonal, and with possible modifications to the synaptic operator; getting back to discrete models, i. e. considering new viewpoints arising from the present continuous approach and examine which of the new results are also valid for the discrete models; discussion about the generalization of the non deterministic, finite temperature dynamics. |
URI : | http://www.repositoriodigital.ipn.mx/handle/123456789/15500 |
ISSN : | 1405-5546 |
Aparece en las colecciones: | Revistas |
Ficheros en este ítem:
Fichero | Descripción | Tamaño | Formato | |
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v13no2_Art03.pdf | 1.52 MB | Adobe PDF | Visualizar/Abrir |
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