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Cited by 18

The DOI matches its Crossref record; 60 of the 60 references it cites were found in a registry or an index.

Relevance in the Renormalization Group and in Information Theory

Gordon, Amit, Banerjee, Aditya, Koch-Janusz, Maciej, Ringel, Zohar·2021·Physical Review Letters
DOI 10.1103/physrevlett.126.240601
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Abstract

The analysis of complex physical systems hinges on the ability to extract the relevant degrees of freedom from among the many others. Though much hope is placed in machine learning, it also brings challenges, chief of which is interpretability. It is often unclear what relation, if any, the architecture- and training-dependent learned "relevant" features bear to standard objects of physical theory. Here we report on theoretical results which may help to systematically address this issue: we establish equivalence between the field-theoretic relevance of the renormalization group, and an information-theoretic notion of relevance we define using the information bottleneck (IB) formalism of compression theory. We show analytically that for statistical physical systems described by a field theory the relevant degrees of freedom found using IB compression indeed correspond to operators with the lowest scaling dimensions. We confirm our field theoretic predictions numerically. We study dependence of the IB solutions on the physical symmetries of the data. Our findings provide a dictionary connecting two distinct theoretical toolboxes, and an example of constructively incorporating physical interpretability in applications of deep learning in physics.

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Cites

Research works printed but not linked: 4

  1. N. Tishby, 2001, Proceedings of the 37th Allerton Conference on Communication, Control and Computation
  2. A. B. Zamolodchikov, 1986, JETP Lett., 43, 730
  3. S. Hassanpour, 2017, Proceedings of the 11th International ITG Conference on Systems, Communications and Coding, SCC 2017
  4. S. Still, 2004, Advances in Neural Information Processing Systems

Metadata

Authors
Gordon, A., Banerjee, A., Koch-Janusz, M., & Ringel, Z.
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2021-06-17
Volume
126
Issue
24
ISSN
  • 0031-9007
  • 1079-7114
DOI
10.1103/physrevlett.126.240601
Cited by
18
References
60
Language
en
Licence
link.aps.org/licenses/aps-default-license (vor)
Funders
  • Israel Science Foundation (2250/19, 1466/15, 820314)
  • Eidgenössische Technische Hochschule Zürich
  • Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
  • National Center of Competence in Research Affective Sciences - Emotions in Individual Behaviour and Social Processes
  • National Center of Competence in Research Quantum Science and Technology
  • H2020 European Research Council (771503)
  • H2020 Marie Skłodowska-Curie Actions (896004)

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