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Quantum field-theoretic machine learning

Dimitrios Bachtis, Gert Aarts Orcid Logo, Biagio Lucini Orcid Logo

Physical Review D, Volume: 103, Issue: 7

Swansea University Authors: Dimitrios Bachtis, Gert Aarts Orcid Logo, Biagio Lucini Orcid Logo

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DOI (Published version): 10.1103/physrevd.103.074510

Abstract

We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the ϕ4 scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as...

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Published in: Physical Review D
ISSN: 2470-0010 2470-0029
Published: American Physical Society (APS) 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa56753
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Specifically, we demonstrate that the &#x3D5;4 scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the &#x3D5;4 theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the &#x3D5;4 theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.</abstract><type>Journal Article</type><journal>Physical Review D</journal><volume>103</volume><journalNumber>7</journalNumber><paginationStart/><paginationEnd/><publisher>American Physical Society (APS)</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>2470-0010</issnPrint><issnElectronic>2470-0029</issnElectronic><keywords>lattice field theory, artificial neural networks, probability theory</keywords><publishedDay>23</publishedDay><publishedMonth>4</publishedMonth><publishedYear>2021</publishedYear><publishedDate>2021-04-23</publishedDate><doi>10.1103/physrevd.103.074510</doi><url/><notes/><college>COLLEGE NANME</college><department>Physics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SPH</DepartmentCode><institution>Swansea University</institution><apcterm>External research funder(s) paid the OA fee (includes OA grants disbursed by the Library)</apcterm><funders>The authors received funding from the European Research Council (ERC) under the European Union&#x2019;s Horizon 2020 research and innovation programme under grant agreement No. 813942. The work of G. A. and B. L. has been supported in part by the UKRI Science and Technology Facilities Council (STFC) Consolidated Grant No. ST/P00055X/1. The work of B. L. is further supported in part by the Royal Society Wolfson Research Merit Award No. WM170010 and by the Leverhulme Foundation Research Fellowship RF-2020-461\9. Numerical simulations have been performed on the Swansea SUNBIRD system. This system is part of the Supercomputing Wales project, which is part-funded by the European Regional Development Fund (ERDF) via Welsh Government. 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spelling 2022-11-11T14:47:11.7959947 v2 56753 2021-04-28 Quantum field-theoretic machine learning 91a311a58d3f8badc779f0ffa6d0ca3d Dimitrios Bachtis Dimitrios Bachtis true false 1ba0dad382dfe18348ec32fc65f3f3de 0000-0002-6038-3782 Gert Aarts Gert Aarts true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 2021-04-28 SPH We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the ϕ4 scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the ϕ4 theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the ϕ4 theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory. Journal Article Physical Review D 103 7 American Physical Society (APS) 2470-0010 2470-0029 lattice field theory, artificial neural networks, probability theory 23 4 2021 2021-04-23 10.1103/physrevd.103.074510 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University External research funder(s) paid the OA fee (includes OA grants disbursed by the Library) The authors received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 813942. The work of G. A. and B. L. has been supported in part by the UKRI Science and Technology Facilities Council (STFC) Consolidated Grant No. ST/P00055X/1. The work of B. L. is further supported in part by the Royal Society Wolfson Research Merit Award No. WM170010 and by the Leverhulme Foundation Research Fellowship RF-2020-461\9. Numerical simulations have been performed on the Swansea SUNBIRD system. This system is part of the Supercomputing Wales project, which is part-funded by the European Regional Development Fund (ERDF) via Welsh Government. We thank European Cooperation in Science and Technology Action CA15213 THOR for support. 2022-11-11T14:47:11.7959947 2021-04-28T11:12:45.3836183 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Dimitrios Bachtis 1 Gert Aarts 0000-0002-6038-3782 2 Biagio Lucini 0000-0001-8974-8266 3 56753__19778__fc56dccc45844286affd58fe88054ace.pdf PhysRevD.103.074510.pdf 2021-04-29T14:51:25.6760289 Output 979736 application/pdf Version of Record true Released under the terms of the Creative Commons Attribution 4.0 International license true eng https://creativecommons.org/licenses/by/4.0/
title Quantum field-theoretic machine learning
spellingShingle Quantum field-theoretic machine learning
Dimitrios Bachtis
Gert Aarts
Biagio Lucini
title_short Quantum field-theoretic machine learning
title_full Quantum field-theoretic machine learning
title_fullStr Quantum field-theoretic machine learning
title_full_unstemmed Quantum field-theoretic machine learning
title_sort Quantum field-theoretic machine learning
author_id_str_mv 91a311a58d3f8badc779f0ffa6d0ca3d
1ba0dad382dfe18348ec32fc65f3f3de
7e6fcfe060e07a351090e2a8aba363cf
author_id_fullname_str_mv 91a311a58d3f8badc779f0ffa6d0ca3d_***_Dimitrios Bachtis
1ba0dad382dfe18348ec32fc65f3f3de_***_Gert Aarts
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
author Dimitrios Bachtis
Gert Aarts
Biagio Lucini
author2 Dimitrios Bachtis
Gert Aarts
Biagio Lucini
format Journal article
container_title Physical Review D
container_volume 103
container_issue 7
publishDate 2021
institution Swansea University
issn 2470-0010
2470-0029
doi_str_mv 10.1103/physrevd.103.074510
publisher American Physical Society (APS)
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the ϕ4 scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the ϕ4 theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the ϕ4 theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.
published_date 2021-04-23T04:11:57Z
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