Associative memories in infinite dimensional spaces

A generalization of the Little-Hopfield neural network model for associative memories is presented that considers the case of a continuum of processing units. The state space corresponds to an infinite dimensional euclidean space. A dynamics is proposed that minimizes an energy functional that is a...

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Detalles Bibliográficos
Autores principales: Segura, E.C., Perazzo, R.P.J.
Formato: JOUR
Materias:
Associative storage
Correlation methods
State space methods
Autocorrelation
Glauber dynamics
Hopfield models
Infinite dimensional euclidean space
Neural networks
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_13704621_v12_n2_p129_Segura
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_13704621_v12_n2_p129_Segura
record_format dspace
spelling todo:paper_13704621_v12_n2_p129_Segura2023-10-03T16:11:39Z Associative memories in infinite dimensional spaces Segura, E.C. Perazzo, R.P.J. Associative storage Correlation methods State space methods Autocorrelation Glauber dynamics Hopfield models Infinite dimensional euclidean space Neural networks A generalization of the Little-Hopfield neural network model for associative memories is presented that considers the case of a continuum of processing units. The state space corresponds to an infinite dimensional euclidean space. A dynamics is proposed that minimizes an energy functional that is a natural extension of the discrete case. The case in which the synaptic weight operator is defined through the autocorrelation rule (Hebb rule) with orthogonal memories is analyzed. We also consider the case of memories that are not orthogonal. Finally, we discuss the generalization of the non deterministic, finite temperature dynamics. Fil:Segura, E.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Perazzo, R.P.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_13704621_v12_n2_p129_Segura
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Associative storage
Correlation methods
State space methods
Autocorrelation
Glauber dynamics
Hopfield models
Infinite dimensional euclidean space
Neural networks
spellingShingle Associative storage
Correlation methods
State space methods
Autocorrelation
Glauber dynamics
Hopfield models
Infinite dimensional euclidean space
Neural networks
Segura, E.C.
Perazzo, R.P.J.
Associative memories in infinite dimensional spaces
topic_facet Associative storage
Correlation methods
State space methods
Autocorrelation
Glauber dynamics
Hopfield models
Infinite dimensional euclidean space
Neural networks
description A generalization of the Little-Hopfield neural network model for associative memories is presented that considers the case of a continuum of processing units. The state space corresponds to an infinite dimensional euclidean space. A dynamics is proposed that minimizes an energy functional that is a natural extension of the discrete case. The case in which the synaptic weight operator is defined through the autocorrelation rule (Hebb rule) with orthogonal memories is analyzed. We also consider the case of memories that are not orthogonal. Finally, we discuss the generalization of the non deterministic, finite temperature dynamics.
format JOUR
author Segura, E.C.
Perazzo, R.P.J.
author_facet Segura, E.C.
Perazzo, R.P.J.
author_sort Segura, E.C.
title Associative memories in infinite dimensional spaces
title_short Associative memories in infinite dimensional spaces
title_full Associative memories in infinite dimensional spaces
title_fullStr Associative memories in infinite dimensional spaces
title_full_unstemmed Associative memories in infinite dimensional spaces
title_sort associative memories in infinite dimensional spaces
url http://hdl.handle.net/20.500.12110/paper_13704621_v12_n2_p129_Segura
work_keys_str_mv AT seguraec associativememoriesininfinitedimensionalspaces
AT perazzorpj associativememoriesininfinitedimensionalspaces
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