Mutual information, neural networks and the renormalization group

Maciej Koch-Janusz*, Zohar Ringel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

118 Scopus citations


Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains ‘slow’ degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

Original languageAmerican English
Pages (from-to)578-582
Number of pages5
JournalNature Physics
Issue number6
StatePublished - 1 Jun 2018

Bibliographical note

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© 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.


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