Feature extraction of machine learning and phase transition point of Ising model

TL;DR

This paper investigates how a trained Restricted Boltzmann Machine (RBM) extracts features from Ising model configurations and how its iterative reconstruction flow can approach the phase transition point, revealing insights into feature representation.

Contribution

It introduces a method to analyze RBM feature extraction and demonstrates the RBM flow's tendency to approach the Ising model's phase transition point, supported by weight matrix analysis.

Findings

RBM flow can approach the phase transition point T_c

Extracted features are emphasized in reconstructed configurations

Weight matrix analysis supports the conjecture about fixed points

Abstract

We study the features extracted by the Restricted Boltzmann Machine (RBM) when it is trained with spin configurations of Ising model at various temperatures. Using the trained RBM, we obtain the flow of iterative reconstructions (RBM flow) of the spin configurations and find that in some cases the flow approaches the phase transition point $T=T_c$ in Ising model. Since the extracted features are emphasized in the reconstructed configurations, the configurations at such a fixed point should describe nothing but the extracted features. Then we investigate the dependence of the fixed point on various parameters and conjecture the condition where the fixed point of the RBM flow is at the phase transition point. We also provide supporting evidence for the conjecture by analyzing the weight matrix of the trained RBM.