Multitasking network with fast noise

TL;DR

This paper explores the phase diagram of a multitasking associative network with noise and pattern dilution, revealing diverse stable states and advancing understanding of parallel processing in neural networks.

Contribution

It provides a comprehensive analytical and numerical analysis of the phase diagram for a multitasking network considering noise and pattern dilution, highlighting the variety of stable states.

Findings

Identification of multiple stable states including pure, parallel, hierarchical, and symmetric mixtures.

Development of self-consistent equations for order parameters using PDE techniques.

Complete mapping of the phase diagram with stability analysis.

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, among which 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, allows us to get the self-consistencies for the order parameters. Such self-consistence equations are then solved and the solutions are further checked through stability theory to catalog their organizations into the phase diagram, which is completely outlined at the end. This is a further step toward the understanding of spontaneous parallel processing in associative networks.