In this work, we introduce and investigate the properties of the “relativistic” Hopfield model endowed with temporally correlated patterns. First, we review the “relativistic” Hopfield model and we briefly describe the experimental evidence underlying correlation among patterns. Then, we face the study of the resulting model exploiting statistical-mechanics tools in a low-load regime. More precisely, we prove the existence of the thermodynamic limit of the related free energy and we derive the self-consistence equations for its order parameters. These equations are solved numerically to get a phase diagram describing the performance of the system as an associative memory as a function of its intrinsic parameters (i.e., the degree of noise and of correlation among patterns). We find that beyond the standard retrieval and ergodic phases, the relativistic system exhibits correlated and symmetric regions, which are genuine effects of temporal correlation, whose width is, respectively, reduced and increased with respect to the classical case.

The relativistic Hopfield model with correlated patterns / Agliari, Elena; Fachechi, Alberto; Marullo, Chiara. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 61:12(2020), p. 123301. [10.1063/5.0010049]

The relativistic Hopfield model with correlated patterns

Agliari, Elena
Primo
;
Fachechi, Alberto;Marullo, Chiara
2020

Abstract

In this work, we introduce and investigate the properties of the “relativistic” Hopfield model endowed with temporally correlated patterns. First, we review the “relativistic” Hopfield model and we briefly describe the experimental evidence underlying correlation among patterns. Then, we face the study of the resulting model exploiting statistical-mechanics tools in a low-load regime. More precisely, we prove the existence of the thermodynamic limit of the related free energy and we derive the self-consistence equations for its order parameters. These equations are solved numerically to get a phase diagram describing the performance of the system as an associative memory as a function of its intrinsic parameters (i.e., the degree of noise and of correlation among patterns). We find that beyond the standard retrieval and ergodic phases, the relativistic system exhibits correlated and symmetric regions, which are genuine effects of temporal correlation, whose width is, respectively, reduced and increased with respect to the classical case.
2020
neural network; statistical mechanics; disordered systems
01 Pubblicazione su rivista::01a Articolo in rivista
The relativistic Hopfield model with correlated patterns / Agliari, Elena; Fachechi, Alberto; Marullo, Chiara. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 61:12(2020), p. 123301. [10.1063/5.0010049]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1469562
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