Neural Network Renormalization Group

TL;DR

This paper introduces a variational renormalization group method using deep generative models with normalizing flows, enabling hierarchical transformations and efficient sampling of physical systems.

Contribution

It develops a novel neural network-based RG framework with exact likelihood and unbiased training, linking deep generative models to physical renormalization techniques.

Findings

Identified independent collective variables in the Ising model.

Performed accelerated hybrid Monte Carlo sampling in latent space.

Provided a variational upper bound of the physical free energy.

Abstract

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