Bistable Gradient Networks II: Storage Capacity and Behaviour Near Saturation

TL;DR

This paper investigates the storage capacity and retrieval behavior of Bistable Gradient Networks, revealing phase transitions at strong coupling and stable memory at high load with some imperfections at weak coupling.

Contribution

It introduces a numerical analysis of Bistable Gradient Networks' storage limits and behavior near saturation, highlighting phase transitions and stability conditions.

Findings

First-order memory blackout transition at strong coupling

Stable pattern retrieval at high load with weak coupling

Enhanced storage capacity with imperfect pattern retrieval

Abstract

We examine numerically the storage capacity and the behaviour near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the Bistable Gradient Network (BGN). For strong coupling, we find evidence of a first-order "memory blackout" phase transition as in the Hopfield network. For weak coupling, on the other hand, there is no evidence of such a transition and memorized patterns can be stable even at high levels of loading. The enhanced storage capacity comes, however, at the cost of imperfect retrieval of the patterns from corrupted versions.