title: Multitasking attractor networks with neuronal threshold noise.
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.
authors.affiliation: Università di Parma, Dipartimento di Fisica, Italy; Università di Parma, INFN Gruppo di Parma, Italy.
authors.forename: Elena
authors.initials: E
authors.lastname: Agliari
authors.forename: Adriano
authors.initials: A
authors.lastname: Barra
authors.forename: Andrea
authors.initials: A
authors.lastname: Galluzzi
authors.forename: Marco
authors.initials: M
authors.lastname: Isopi
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D005583:Fourier Analysis; D015233:Models, Statistical; D009010:Monte Carlo Method; D016571:Neural Networks, Computer; D060388:Support Vector Machine; D013816:Thermodynamics
keywords: Hopfield model; Multitasking networks; Statistical mechanics