Associative Memory in a Continuous Metric Space: A Theoretical Foundation
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Redalyc
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| Natura: | Artículo científico |
| Lingua: | en |
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Instituto Politécnico Nacional
2009
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| _version_ | 1876478800700637184 |
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| author | Enrique Carlos Segura |
| author_facet | Enrique Carlos Segura |
| contents | Associative Memory in a Continuous Metric Space: A Theoretical Foundation Enrique Carlos Segura Computación stability Hopfield model Glauber dynamics dynamical systems Associative memory 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. 2009 artículo científico 1405-5546 https://www.redalyc.org/articulo.oa?id=61519181004 en http://www.redalyc.org/revista.oa?id=615 Computación y Sistemas application/pdf Instituto Politécnico Nacional Computación y Sistemas (México) Num.2 Vol.13 |
| format | Artículo científico |
| id | redalyc_61519181004 |
| institution | Redalyc |
| language | en |
| publishDate | 2009 |
| publisher | Instituto Politécnico Nacional |
| spellingShingle | Associative Memory in a Continuous Metric Space: A Theoretical Foundation Enrique Carlos Segura Computación stability Hopfield model Glauber dynamics dynamical systems Associative memory Associative Memory in a Continuous Metric Space: A Theoretical Foundation Enrique Carlos Segura Computación stability Hopfield model Glauber dynamics dynamical systems Associative memory 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. 2009 artículo científico 1405-5546 https://www.redalyc.org/articulo.oa?id=61519181004 en http://www.redalyc.org/revista.oa?id=615 Computación y Sistemas application/pdf Instituto Politécnico Nacional Computación y Sistemas (México) Num.2 Vol.13 |
| title | Associative Memory in a Continuous Metric Space: A Theoretical Foundation |
| topic | Computación stability Hopfield model Glauber dynamics dynamical systems Associative memory |
| url | https://www.redalyc.org/articulo.oa?id=61519181004 |