Neural Monte Carlo Renormalization Group

TL;DR

This paper introduces a neural Monte Carlo RG algorithm that learns optimal real-space RG transformations directly from data, enabling computation of RG flows and critical exponents without prior physical knowledge.

Contribution

It establishes a novel connection between RG transformations and deep learning architectures, allowing automatic learning of optimal transformations.

Findings

Successfully learns RG transformations from data

Enables direct computation of RG flow and critical exponents

Maximizes mutual information between coarse-grained regions

Abstract

The key idea behind the renormalization group (RG) transformation is that properties of physical systems with very different microscopic makeups can be characterized by a few universal parameters. However, finding the optimal RG transformation remains difficult due to the many possible choices of the weight factors in the RG procedure. Here we show, by identifying the conditional distribution in the restricted Boltzmann machine (RBM) and the weight factor distribution in the RG procedure, an optimal real-space RG transformation can be learned without prior knowledge of the physical system. This neural Monte Carlo RG algorithm allows for direct computation of the RG flow and critical exponents. This scheme naturally generates a transformation that maximizes the real-space mutual information between the coarse-grained region and the environment. Our results establish a solid connection between the RG transformation in physics and the deep architecture in machine learning, paving the way to further interdisciplinary research.