Among the performance-enhancing procedures for Hopfield-type networks that implement associative memory, Hebbian Unlearning (or dreaming) strikes for its simplicity and its clear biological interpretation. Yet, it does not easily lend itself to a clear analytical understanding. Here we show how Hebbian Unlearning can be effectively described in terms of a simple evolution of the spectrum and the eigenvectors of the coupling matrix. We use these ideas to design new dreaming algorithms that are effective from a computational point of view, and are analytically far more transparent than the original scheme.
@article{arxiv.2308.13445,
title = {Eigenvector Dreaming},
author = {Marco Benedetti and Louis Carillo and Enzo Marinari and Marc Mèzard},
journal= {arXiv preprint arXiv:2308.13445},
year = {2023}
}