# On a model of associative memory with huge storage capacity

## TL;DR

This paper proves that a generalized Hopfield model with exponential interaction functions achieves exponential storage capacity while maintaining large basins of attraction, significantly enhancing associative memory models.

## Contribution

It confirms Krotov and Hopfield's claim by proving exponential storage capacity and analyzes the basin sizes in the generalized model.

## Key findings

- Exponential storage capacity with exponential interaction functions.
- Basins of attraction remain nearly as large as in the standard Hopfield model.
- Validation of the generalized model's improved capacity.

## Abstract

In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model. We prove this claim and take the "limit" as the degree of the polynomial becomes infinite, i.e. an exponential interaction function. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.