Restricted Boltzmann machines for the long range Ising models

2016/12/01 by Kenichi Aoki, Ken-Ichi Aoki, Tamao Kobayashi · 4 citations
Mathematics · Physics and Astronomy · #Artificial intelligence #Block (permutation group theory) #Boltzmann constant #Boltzmann machine #Combinatorics #Computer science #Decimation #Deep learning #Dimension (graph theory) #Ising model #Magnetic field #Materials science #Mathematics #Model Reduction and Neural Networks #Physics #Quantum many-body systems #Quantum mechanics #Range (aeronautics) #Restricted Boltzmann machine #Set (abstract data type) #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1142/s0217984916504017

published as Mod. Phys. Lett. B 30,1650401(2016) 10pages · 13 pages,6 figures

openalex publication_date 2016/12/01 · arxiv created 2017/01/01 · arxiv updated 2017/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We set up restricted Boltzmann machines (RBM) to reproduce the long range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of configuration with probability (CwP). The quality of resultant RBM is evaluated through the susceptibility with respect to the magnetic external field. We compare the results with those by block decimation renormalization group (BDRG) method, and our RBM clear the test with satisfactory precision.

Citations

• The renormalization group: Critical phenomena and the Kondo problem
• Training Products of Experts by Minimizing Contrastive Divergence
• Mastering the game of Go with deep neural networks and tree search

Cited by

• Scale-invariant feature extraction of neural network and renormalization group flow
• Machine Learning Detection of Bell Nonlocality in Quantum Many-Body Systems
• Thermodynamics and feature extraction by machine learning
• Machine learning of phase transitions in the percolation andXYmodels