Storage Capacity of Extremely Diluted Hopfield Model

TL;DR

This paper investigates how systematically diluting synapses in an extremely diluted Hopfield Model affects its storage capacity, finding that strategic dilution can enhance capacity close to theoretical limits.

Contribution

It introduces a systematic method for synapse dilution based on dominant contributions, showing capacity improvements aligned with mean-field predictions.

Findings

Critical storage capacity increases with dilution

Capacity approaches mean-field theoretical values

Dilution effectiveness depends on original capacity and dilution fraction

Abstract

The storage capacity of the extremely diluted Hopfield Model is studied by using Monte Carlo techniques. In this work, instead of diluting the synapses according to a given distribution, the dilution of the synapses is obtained systematically by retaining only the synapses with dominant contributions. It is observed that by using the prescribed dilution method the critical storage capacity of the system increases with decreasing number of synapses per neuron reaching almost the value obtained from mean-field calculations. It is also shown that the increase of the storage capacity of the diluted system depends on the storage capacity of the fully connected Hopfield Model and the fraction of the diluted synapses.