Statistical physics through the lens of real-space mutual information

Abstract

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 evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building.

arXiv commentVersion accepted for publication in Physical Review Letters. See also the companion manuscript arXiv:2103.16887 "Symmetries and phase diagrams with real-space mutual estimation neural estimation"

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Cited by in corpus (12)

• Neural Information Squeezer for Causal Emergence
• Symmetries and phase diagrams with real-space mutual information neural estimation
• Lattice physics approaches for neural networks
• Network Renormalization
• Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model
• Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter
• Superconducting fluctuations and charge-4$e$ plaquette state at strong coupling
• Compression theory for inhomogeneous systems
• Bayesian RG Flow in Neural Network Field Theories
• Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty
• Dreaming up scale invariance via inverse renormalization group
• Minimizing couplings in renormalization by preserving short-range mutual information