Restricted Boltzmann Machine Flows and The Critical Temperature of Ising models

Description

Code for Restricted Boltzmann Machine Flows and The Critical Temperature of Ising models.

Paper link: arXiv:2006.10176

Prerequisites

• python >= 3.6
• pytorch
• scikit-learn
• numpy
• matplotlib
• pandas
• scipy
• tensorboardX

Typically, Anaconda distribution for Python >= 3.6 is enough. If you choose to use tensorboardX visualization during Restricted Boltzmann Machine (RBM) training, it is necessary to install it with pip install tensorboardX.

Usage

The main discussion and the flows are presented in the notebooks:

• main_discussion_L010.ipynb.
• main_discussion_L100.ipynb.

Further analysis about learned weight matrices:

• weight_analysis_L010.ipynb.
• weight_analysis_L036.ipynb.
• weight_analysis_L048.ipynb.
• weight_analysis_L100.ipynb.
• weight_analysis_comparing_L.ipynb.

Folders with data and saved trained models:

• data: Monte Carlo (MC) samples for the Ising model in a square lattice.
• NN_trained_models: trained neural network (NN) thermometers.
• RBM_trained_models: trained RBMs.
• RBM_flows: RBM flows.
• runs: tensorboardX files if you choose tensorboard=True on rbm.py.
• figures: saved plots.
• weight_analysis: singular value and eigenvalue decompositions.

The classes for the MC sampling, the NN thermometer and the RBM are presented in the folder modules:

• mc_ising2d.py
• mc_ising2d_MF.py
• net.py
• rbm.py (for GPU computation: use_cuda=True)

NN and RBM training in the folders:

• training_NN_thermometer
• training_RBM

License

See LICENSE.

References

• Scale-invariant feature extraction of neural network and renormalization group flow, Phys. Rev. E 97, 053304 (2018).
• An exact mapping between the Variational Renormalization Group and Deep Learning, arXiv:1410.3831 (2014).
• Deep learning and the renormalization group, arXiv:1301.3124 (2013).
• A high-bias, low-variance introduction to machine learning for physicists, Physics Reports, https://doi.org/10.1016/j.physrep.2019.03.001 (2019).