We consider the multitasking associative network in the low-storage limit and we study its phase diagram with respect to the noise level T and the degree d of dilution in pattern entries. We find that the system is characterized by a rich variety of stable states, including pure states, parallel retrieval states, hierarchically organized states and symmetric mixtures (remarkably, both even and odd), whose complexity increases as the number of patterns P grows. The analysis is performed both analytically and numerically: Exploiting techniques based on partial differential equations, we are able to get the self-consistencies for the order parameters. Such self-consistency equations are then solved and the solutions are further checked through stability theory to catalog their organizations into the phase diagram, which is outlined at the end. This is a further step towards the understanding of spontaneous parallel processing in associative networks. © 2013 Elsevier Ltd.
Multitasking attractor networks with neuronal threshold noise / Agliari, Elena; Barra, Adriano; Galluzzi, Andrea; Isopi, Marco. - In: NEURAL NETWORKS. - ISSN 0893-6080. - STAMPA. - 49:(2014), pp. 19-29. [10.1016/j.neunet.2013.09.008]
Multitasking attractor networks with neuronal threshold noise
AGLIARI, ELENA;BARRA, ADRIANO;GALLUZZI, ANDREA;ISOPI, Marco
2014
Abstract
We consider the multitasking associative network in the low-storage limit and we study its phase diagram with respect to the noise level T and the degree d of dilution in pattern entries. We find that the system is characterized by a rich variety of stable states, including pure states, parallel retrieval states, hierarchically organized states and symmetric mixtures (remarkably, both even and odd), whose complexity increases as the number of patterns P grows. The analysis is performed both analytically and numerically: Exploiting techniques based on partial differential equations, we are able to get the self-consistencies for the order parameters. Such self-consistency equations are then solved and the solutions are further checked through stability theory to catalog their organizations into the phase diagram, which is outlined at the end. This is a further step towards the understanding of spontaneous parallel processing in associative networks. © 2013 Elsevier Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.