Finite Connectivity Attractor Neural Networks

TL;DR

This paper analyzes finite connectivity attractor neural networks using replica symmetry, deriving phase diagrams and transition lines, revealing continuous phase transitions between paramagnetic, retrieval, and spin-glass phases.

Contribution

It introduces an integral equation for order parameters in finite connectivity neural networks and performs a bifurcation analysis to map phase transitions.

Findings

Identifies phase transition lines in the phase diagram.

Derives an integral equation for order parameters.

Shows all phase transitions are continuous.

Abstract

We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric (RS) approximation. A bifurcation analysis of this equation reveals the locations of the paramagnetic to recall and paramagnetic to spin-glass transition lines in the phase diagram. The line separating the retrieval phase from the spin-glass phase is calculated at zero temperature. All phase transitions are found to be continuous.