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

arXiv: https://arxiv.org/abs/2201.00032 · HTML: https://mlsanity.com/paper/2201.00032/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2021.

## Built on by (most cited first, 9 of 9)

- [Phase transitions in the mini-batch size for sparse and dense two-layer neural networks](https://mlsanity.com/paper/2305.06435/) (2023)
- [Matrix factorization with neural networks](https://mlsanity.com/paper/2212.02105/) (2022)
- [Training neural networks with structured noise improves classification and generalization](https://mlsanity.com/paper/2302.13417/) (2023)
- [On the phase diagram of extensive-rank symmetric matrix denoising beyond rotational invariance](https://mlsanity.com/paper/2411.01974/) (2024)
- [Regularization, early-stopping and dreaming: a Hopfield-like setup to address generalization and overfitting](https://mlsanity.com/paper/2308.01421/) (2023)
- [The Decimation Scheme for Symmetric Matrix Factorization](https://mlsanity.com/paper/2307.16564/) (2023)
- [Pseudo-likelihood produces associative memories able to generalize, even for asymmetric couplings](https://mlsanity.com/paper/2507.05147/) (2025)
- [Statistical Mechanics and Artificial Neural Networks: Principles, Models, and Applications](https://mlsanity.com/paper/2405.10957/) (2024)
- [Language Diffusion Models are Associative Memories Capable of Retrieving Unseen Data](https://mlsanity.com/paper/2604.26841/) (2026)

## Abstract (arXiv)

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.