Comment on "Fastest learning in small-world neural networks"

TL;DR

This paper corrects a previous study on small-world neural networks by recalculating local connectivity lengths and re-evaluating learning performance, ultimately challenging the claim that rewiring improves learning efficiency.

Contribution

It provides corrected calculations of local connectivity lengths and re-assesses the impact of rewiring on neural network learning, disputing prior claims of small-world benefits.

Findings

Rewiring does not produce small-world connectivity in FNNs.

Rewiring does not consistently reduce learning errors across different training sets.

Previous claims of improved learning through rewiring are invalidated.

Abstract

This comment reexamines Simard et al.'s work in [D. Simard, L. Nadeau, H. Kroger, Phys. Lett. A 336 (2005) 8-15]. We found that Simard et al. calculated mistakenly the local connectivity lengths Dlocal of networks. The right results of Dlocal are presented and the supervised learning performance of feedforward neural networks (FNNs) with different rewirings are re-investigated in this comment. This comment discredits Simard et al's work by two conclusions: 1) Rewiring connections of FNNs cannot generate networks with small-world connectivity; 2) For different training sets, there do not exist networks with a certain number of rewirings generating reduced learning errors than networks with other numbers of rewiring.