NeuralRG

Pytorch implement of arXiv paper: Shuo-Hui Li and Lei Wang, Neural Network Renormalization Group arXiv:1802.02840.

NeuralRG is a deep generative model using variational renormalization group approach, it's also a kind of normalizing flow, it is composed by layers of bijectors (In our implementation, we use realNVP). After training, it can generate statistically independent physical configurations with tractable likelihood via directly sampling.

How does NeuralRG work

In NeuralRG Network(a), we use realNVP (b) networks as building blocks, realNVP is a kind of bijectors(a normalizing flow), they can transform one distribution into other distribution and revert this process. For multi-in-multi-out blocks, we call they disentanglers(gray blocks in (a)), and for multi-in-single-out blocks, we can they decimators(white blocks in (a)). And stacking multiple layers of these blocks into a hierarchical structure forms NeuralRG network, so NeuralRG is also a bijector. In inference process, each layer tries to "separate" entangled variables into independent variables, and at layers composed of decimators, we only keep one of these independent variables, this is renormalization group.

The structure we used to construct realNVP networks into NeuralRG network is inspired by multi-scale entanglement renormalization ansatz (MERA), as shown in (a). Also, the process of variable going through our network can be viewed as a renormalization process.

The resulted effect of a trained NeuralRG network can be visualized using gradients plot (a) and MI plot of variables of the same layer (b)(c). The latent variables of NeuralRG appears to be a nonlinear and adaptive generalization of wavelet basis.

How to Run

Train

Use main.py to train model. Options available are:

• folder specifies saving path. At that path a parameters.hdf5 will be created to keep training parameters, a pic folder will be created to keep plots, a records folder will be created to keep saved HMC records, and a savings folder to save models in.
• name specifies model's name. If not specified, a name will be created according to training parameters.
• epochs, batch, lr, savePeriod are the number of training epochs, batch size, learning rate, the number of epochs before saving.
• cuda indicates on which GPU card should the model be trained, the default value is -1, which means running on CPU.
• double indicates if use double float.
• load indicates if load a pre-trained model. If true, will try to find a pre-trained model at where folder suggests. Note that if true all other parameters will be overwritten with what saved in folder's parameters.hdf5.
• nmlp, nhidden are used to construct MLP networks inside of realNVP networks. nmlp is the number of layers in MLP networks and nhidden is the number of hidden neurons in each layer.
• nlayers is used to construct realNVP networks, it suggests how many layers in each realNVP networks.
• nrepeat is used to construct MERA network, it suggests how many layers of bijectors inside of each layer of MERA network.
• L, d, T are used to construct the Ising model to learn, L is the size of configuration, d is the dimension, and T is the temperature.
• alpha ,symmetry are options about symmetried , symmetrized will be used if use -symmetry option. If -symmetry option is not added, -alpha can add a regulation term to loss to try to inflate symmetry.
• skipHMC is used to skip HMC process during training save memory.

For example, to train the Ising model mentioned in our paper:

python ./main.py -epochs 5000 -folder ./opt/16Ising -batch 512 -nlayers 10 -nmlp 3 -nhidden 10 -L 16 -nrepeat 1 -savePeriod 100 -symmetry

Plot

Use plot.py to plot the loss curve and HMC results. Options available are:

• folder specifies saving path. plot.py will use the data saved in that path to plot. And if save is true, the plot will be saved in folder's pic folder.
• per specifies how many seconds between each refresh.
• show, save specifies if will show/save the plot.
• exact specifies the exact result of HMC.

For example, to plot along with the training process mentioned above:

python ./plot.py -folder ./opt/16Ising -per 30 -exact 0.544445

Train multiple models

Change settings in settings.py to train diffierent models in different temperatures and different depths. Then python core.py will read these settings and train these models. Figure of relative loss of different temperatures and depths can be plotted using paperplot/plotCore.py.

Citation

If you use this code for your research, please cite our paper:

@article{neuralRG,
  Author = {Shuo-Hui Li and Lei Wang},
  Title = {Neural Network Renormalization Group},
  Year = {2018},
  Eprint = {arXiv:1802.02840},
}

Contact

For questions and suggestions, contact Shuo-Hui Li at [email protected].