Influence of topology on the performance of a neural network

TL;DR

This study compares how different neural network topologies, especially scale-free networks, affect the ability to store and retrieve patterns, revealing that scale-free topologies outperform random networks under certain conditions.

Contribution

It demonstrates that scale-free topologies enhance storage and retrieval capacity in attractor neural networks compared to random-diluted networks, especially at finite temperature.

Findings

Scale-free networks have higher capacity than random networks.

Performance of scale-free networks improves with higher power-law exponent.

Scale-free topology benefits are discussed for biological and artificial systems.

Abstract

We studied the computational properties of an attractor neural network (ANN) with different network topologies. Though fully connected neural networks exhibit, in general, a good performance, they are biologically unrealistic, as it is unlikely that natural evolution leads to such a large connectivity. We demonstrate that, at finite temperature, the capacity to store and retrieve binary patterns is higher for ANN with scale--free (SF) topology than for highly random--diluted Hopfield networks with the same number of synapses. We also show that, at zero temperature, the relative performance of the SF network increases with increasing values of the distribution power-law exponent. Some consequences and possible applications of our findings are discussed.