Disappearance of Spurious States in Analog Associative Memories

TL;DR

This paper demonstrates that symmetric mixture states are generally unstable in autoassociative networks with threshold-linear units, except in specific binary coding scenarios where certain mixtures can be stable.

Contribution

It reveals the instability of symmetric mixture states in threshold-linear networks and identifies conditions under which some mixtures are stable.

Findings

Symmetric mixture states are almost never stable in these networks.

Binary coding schemes can stabilize 2- and 3-mixture states.

Stability depends on specific parameter regions.

Abstract

We show that symmetric n-mixture states, when they exist, are almost never stable in autoassociative networks with threshold-linear units. Only with a binary coding scheme we could find a limited region of the parameter space in which either 2-mixtures or 3-mixtures are stable attractors of the dynamics.