  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.
