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

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.

18 pages, 12 figures

References in corpus (10)

• Very Deep Convolutional Networks for Large-Scale Image Recognition
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• An exact mapping between the Variational Renormalization Group and Deep Learning
• Neural Network Renormalization Group
• Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow
• Super-resolving the Ising model with convolutional neural networks
• Thermodynamics and Feature Extraction by Machine Learning
• Machine learning determination of dynamical parameters: The Ising model case
• Deep learning and the renormalization group
• Restricted Boltzmann Machine Flows and The Critical Temperature of Ising models