# High storage capacity in the Hopfield model with auto-interactions - stability analysis

## TL;DR

This paper analyzes the stability of new fixed points in the Hopfield model with auto-interactions, revealing their instability and limited usefulness for reliable pattern storage despite high capacity claims.

## Contribution

It provides a stability analysis of recently proposed high-capacity fixed points in the Hopfield model, highlighting their instability and limitations for associative memory applications.

## Key findings

- New fixed points are unstable under small perturbations
- Errors in stored patterns tend to increase during retrieval
- High storage capacity fixed points are of limited practical use

## Abstract

Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that they exhibit instabilities for small perturbations and are therefore of limited value as associative memories. Moreover, a large deviations approach also shows that errors introduced to the original patterns induce additional errors and increased corruption with respect to the stored patterns.