Comment on ``Capacity of the Hopfield model''

TL;DR

This paper critiques a recent claim about the Hopfield model's capacity, arguing that the proof is flawed and does not provide rigorous results as claimed.

Contribution

It provides a critical analysis showing the errors in Feng and Tirozzi's proof and clarifies that their approach lacks mathematical rigor.

Findings

Feng and Tirozzi's results are incorrect.

Their proof contains errors that invalidate their conclusions.

The approach used does not establish rigorous results.

Abstract

In a recent paper ``The capacity of the Hopfield model, J. Feng and B. Tirozzi claim to prove rigorous results on the storage capacity that are in conflict with the predictions of the replica approach. We show that their results are in error and that their approach, even when the worst mistakes are corrected, is not giving any mathematically rigorous results.