Comment on "Finite size scaling in Neural Networks"

TL;DR

This paper critiques the finite size scaling approach proposed by Nadler and Fink for estimating the storage capacity of Ising perceptrons, demonstrating its inaccuracy with larger system sizes.

Contribution

It provides a faster algorithm to measure storage capacity and shows the limitations of existing finite size scaling methods for small systems.

Findings

Finite size scaling ansatz does not accurately estimate storage capacity.

The new algorithm efficiently handles system sizes up to N=42.

Finite size effects are significant and affect capacity estimates.

Abstract

We use a binary search tree and the simplex algorithm to measure the fraction of patterns that can be stored by an Ising perceptron. The algorithm is much faster than exhaustive search and allows us to obtain accurate statistics up to a system size of N=42. The results show that the finite size scaling ansatz Nadler and Fink suggest in [1] cannot be applied to estimate accurately the storage capacity from small systems. [1] W.Nadler and W.Fink: Phys.Rev.Lett. 78, 555 (1997)