Statistical physics with Real-Space Mutual Information Neural Estimation

  Maciej Koch-Janusz [1,2]  ,  Doruk Efe Gokmen [3]  ,  Sebastian D. Huber [3]  ,  Zohar Ringel [4]  
[1] Department of Physics, University of Zurich
[2] James Franck Institute, University of Chicago
[3] Institute for Theoretical Physics, ETH Zurich
[4] Racah Institute of Physics, Hebrew University of Jerusalem

Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We demonstrate it on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks. The results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building.