Topologically continuous associative memory: A theoretical foundation
We introduce a neural network with associative memory and a 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 Hop-fie...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_97809727_v_n_p112_Segura |
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todo:paper_97809727_v_n_p112_Segura2023-10-03T16:42:54Z Topologically continuous associative memory: A theoretical foundation Segura, E.C. Associative memory Continuous topology Dynamical systems Hopfield model Infinite dimensional state space Stability Associative memories Attraction basin Continuous approach Discrete models Energy functions Euclidean Hopfield models Infinite dimensional Metric spaces Neural systems New results Plausible model Processing units State space Stationary solutions Theoretical foundations Variational approaches Artificial intelligence Associative processing Associative storage Convergence of numerical methods Dynamical systems Topology We introduce a neural network with associative memory and a 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 Hop-field. Thus we integrate two levels of continuity: continuous response units and continuous topology of the neural system, obtaining a more biologically plausible model of associative memory. A theoretical background is provided so as to make this integration consistent. We first present some general results concerning attractors and stationary solutions, including a variational approach for the derivation of the energy function. Then we focus on the case of orthogonal memories, proving theorems on their stability, size of attraction basins and spurious states. Finally, we get 1back to discrete models, i.e. we discuss new viewpoints arising from the present continuous approach and examine which of the new results are also valid for the discrete models. Copyright © 2007 IICAI. CONF info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_97809727_v_n_p112_Segura |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Associative memory Continuous topology Dynamical systems Hopfield model Infinite dimensional state space Stability Associative memories Attraction basin Continuous approach Discrete models Energy functions Euclidean Hopfield models Infinite dimensional Metric spaces Neural systems New results Plausible model Processing units State space Stationary solutions Theoretical foundations Variational approaches Artificial intelligence Associative processing Associative storage Convergence of numerical methods Dynamical systems Topology |
| spellingShingle |
Associative memory Continuous topology Dynamical systems Hopfield model Infinite dimensional state space Stability Associative memories Attraction basin Continuous approach Discrete models Energy functions Euclidean Hopfield models Infinite dimensional Metric spaces Neural systems New results Plausible model Processing units State space Stationary solutions Theoretical foundations Variational approaches Artificial intelligence Associative processing Associative storage Convergence of numerical methods Dynamical systems Topology Segura, E.C. Topologically continuous associative memory: A theoretical foundation |
| topic_facet |
Associative memory Continuous topology Dynamical systems Hopfield model Infinite dimensional state space Stability Associative memories Attraction basin Continuous approach Discrete models Energy functions Euclidean Hopfield models Infinite dimensional Metric spaces Neural systems New results Plausible model Processing units State space Stationary solutions Theoretical foundations Variational approaches Artificial intelligence Associative processing Associative storage Convergence of numerical methods Dynamical systems Topology |
| description |
We introduce a neural network with associative memory and a 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 Hop-field. Thus we integrate two levels of continuity: continuous response units and continuous topology of the neural system, obtaining a more biologically plausible model of associative memory. A theoretical background is provided so as to make this integration consistent. We first present some general results concerning attractors and stationary solutions, including a variational approach for the derivation of the energy function. Then we focus on the case of orthogonal memories, proving theorems on their stability, size of attraction basins and spurious states. Finally, we get 1back to discrete models, i.e. we discuss new viewpoints arising from the present continuous approach and examine which of the new results are also valid for the discrete models. Copyright © 2007 IICAI. |
| format |
CONF |
| author |
Segura, E.C. |
| author_facet |
Segura, E.C. |
| author_sort |
Segura, E.C. |
| title |
Topologically continuous associative memory: A theoretical foundation |
| title_short |
Topologically continuous associative memory: A theoretical foundation |
| title_full |
Topologically continuous associative memory: A theoretical foundation |
| title_fullStr |
Topologically continuous associative memory: A theoretical foundation |
| title_full_unstemmed |
Topologically continuous associative memory: A theoretical foundation |
| title_sort |
topologically continuous associative memory: a theoretical foundation |
| url |
http://hdl.handle.net/20.500.12110/paper_97809727_v_n_p112_Segura |
| work_keys_str_mv |
AT seguraec topologicallycontinuousassociativememoryatheoreticalfoundation |
| _version_ |
1807319948140216320 |