Neural Network Renormalization Group

We present a variational renormalization group (RG) approach based on a reversible generative model with hierarchical architecture. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural ne...

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Veröffentlicht in:Physical review letters Jg. 121; H. 26; S. 260601
Hauptverfasser: Li, Shuo-Hui, Wang, Lei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States American Physical Society 28.12.2018
Schlagworte:
Computer simulation
Distillation
Free energy
Independent variables
Ising model
Mathematical models
Neural networks
Training
Upper bounds
Wavelet analysis
ISSN:0031-9007, 1079-7114, 1079-7114
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Zusammenfassung:We present a variational renormalization group (RG) approach based on a reversible generative model with hierarchical architecture. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural network directly maps independent Gaussian noises to physical configurations following the inverse RG flow. The model has an exact and tractable likelihood, which allows unbiased training and direct access to the renormalized energy function of the latent variables. To train the model, we employ probability density distillation for the bare energy function of the physical problem, in which the training loss provides a variational upper bound of the physical free energy. We demonstrate practical usage of the approach by identifying mutually independent collective variables of the Ising model and performing accelerated hybrid Monte Carlo sampling in the latent space. Lastly, we comment on the connection of the present approach to the wavelet formulation of RG and the modern pursuit of information preserving RG.
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ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.121.260601