On the neural network flow of spin configurations

TL;DR

This paper investigates the neural network flow of spin configurations in the 2D Ising model, challenging previous claims that it converges to the critical point, and analyzes how network hyperparameters influence this flow.

Contribution

It refutes prior claims about the neural network flow reaching the critical point and explores the impact of hyperparameters and data intrinsic dimension on the flow.

Findings

Flow does not converge to the critical point as previously claimed.

Network hyperparameters significantly affect the flow behavior.

Reconstruction error relates to the intrinsic dimension of data.

Abstract

We study the so-called neural network flow of spin configurations in the 2-d Ising ferromagnet. This flow is generated by successive reconstructions of spin configurations, obtained by an artificial neural network like a restricted Boltzmann machine or an autoencoder. It was reported recently that this flow may have a fixed point at the critical temperature of the system, and even allow the computation of critical exponents. Here we focus on the flow produced by a fully-connected autoencoder, and we refute the claim that this flow converges to the critical point of the system by directly measuring physical observables, and showing that the flow strongly depends on the network hyperparameters. We explore the network metric, the reconstruction error, and we relate it to the so called intrinsic dimension of data, to shed light on the origin and properties of the flow.