Associative networks with diluted patterns: dynamical analysis at low and medium load

TL;DR

This paper analyzes the dynamics of associative networks with diluted patterns, revealing how pattern recall and stability depend on temperature, pattern interference, and dilution, with implications for understanding neural network retrieval processes.

Contribution

It provides a detailed dynamical analysis of pattern diluted associative networks, including derivation of order parameter equations and stability analysis across different regimes.

Findings

Symmetric pattern recall occurs below critical temperature without cross-talk.

Pattern cross-talk causes hierarchical retrieval as temperature decreases.

Parallel retrieval degrades gracefully under strong interference.

Abstract

In this work we solve the dynamics of pattern diluted associative networks, evolving via sequential Glauber update. We derive dynamical equations for the order parameters, that quantify the simultaneous pattern recall of the system, and analyse the nature and stability of the stationary solutions by means of linear stability analysis as well as Monte Carlo simulations. We investigate the parallel retrieval capabilities of the system in different regions of the phase space, in particular in the low and medium storage regimes and for finite and extreme pattern dilution. Results show that in the absence of patterns cross-talk, all patterns are recalled symmetrically for any temperature below criticality, while in the presence of pattern cross-talk, symmetric retrieval becomes unstable as temperature is lowered and a hierarchical retrieval takes over. The shape of the hierarchical retrieval occurring at zero temperature is provided. The parallel retrieval capabilities of the network are seen to degrade gracefully in the regime of strong interference, but they are not destroyed.