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Lower bounds on the restitution error in the Hopfield Model
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  • Published: 01 October 2002

Lower bounds on the restitution error in the Hopfield Model

  • Daria Loukianova1 

Probability Theory and Related Fields volume 107, pages 161–176 (1997)Cite this article

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Summary.

This paper contains a first rigorous results at the direction of the converse to Newman's bounds [11] on the storage capacity for the Hopfield model of associative memory. Let \(m\) denote the number of stored patterns and \(N\) that of neurons. Assuming that \(m/N\to \alpha\) as \(N\to\infty \) we show that for \(\alpha>0\) the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value (approximately 0.05) as \(\alpha\to\infty \).

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  1. Equipe d'Analyse et Probabilités, Université d'Evry-Essonne, Bd des Coquibus, F-91025 Evry, France (e-mail: dasha@dmi.univ-evry.fr), Evry, France

    Daria Loukianova

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  1. Daria Loukianova
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Received: 1 November 1994 / In revised form: 16 November 1995

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Loukianova, D. Lower bounds on the restitution error in the Hopfield Model. Probab Theory Relat Fields 107, 161–176 (1997). https://doi.org/10.1007/s004400050081

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  • Published: 01 October 2002

  • Issue Date: February 1997

  • DOI: https://doi.org/10.1007/s004400050081

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  • Mathematics Subject Classification (1991): 60G17, 60F10, 92B20, 68T10
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