Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networks

TL;DR

This paper compares supervised perceptron learning and unsupervised Hebbian unlearning in Hopfield-like networks, showing similar stability and convergence properties, and offers a geometric interpretation of Hebbian unlearning's effectiveness.

Contribution

It provides a detailed comparison of two learning algorithms for neural networks and introduces a geometric perspective to explain Hebbian unlearning's optimal performance.

Findings

Hebbian unlearning and perceptron training have comparable basin sizes.

Both algorithms converge within the same Gardner space region.

A geometric interpretation explains Hebbian unlearning's effectiveness.

Abstract

The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We analyze the stability of the stored memories: basins of attraction obtained by the Hebbian unlearning technique are found to be comparable in size to those obtained in the symmetric perceptron, while the two algorithms are found to converge in the same region of Gardner's space of interactions, having followed similar learning paths. A geometric interpretation of Hebbian unlearning is proposed to explain its optimal performances. Because the Hopfield model is also a prototypical model of disordered magnetic system, it might be possible to translate our results to other models of interest for memory storage in materials.