Neural Monte Carlo renormalization group

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 a systematic way to construct RG transformation for particular systems 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 and the weight factor distribution in the RG procedure, that a valid 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. Our results establish a solid connection between the RG transformation in physics and the deep architecture in machine learning, paving the way for further interdisciplinary research.