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Scalar field restricted Boltzmann machine as an ultraviolet regulator

Gert Aarts Orcid Logo, Biagio Lucini Orcid Logo, Chanju Park

Physical Review D, Volume: 109, Issue: 3

Swansea University Authors: Gert Aarts Orcid Logo, Biagio Lucini Orcid Logo, Chanju Park

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DOI (Published version): 10.1103/physrevd.109.034521

Abstract

Restricted Boltzmann machines (RBMs) are well-known tools used in machine learning to learn probability distribution functions from data. We analyze RBMs with scalar fields on the nodes from the perspective of lattice field theory. Starting with the simplest case of Gaussian fields, we show that the...

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Published in: Physical Review D
ISSN: 2470-0010 2470-0029
Published: American Physical Society (APS) 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa65735
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spelling v2 65735 2024-03-04 Scalar field restricted Boltzmann machine as an ultraviolet regulator 1ba0dad382dfe18348ec32fc65f3f3de 0000-0002-6038-3782 Gert Aarts Gert Aarts true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 60c7e702548bc829b5cbe3040ac41e8e Chanju Park Chanju Park true false 2024-03-04 SPH Restricted Boltzmann machines (RBMs) are well-known tools used in machine learning to learn probability distribution functions from data. We analyze RBMs with scalar fields on the nodes from the perspective of lattice field theory. Starting with the simplest case of Gaussian fields, we show that the RBM acts as an ultraviolet regulator, with the cutoff determined by either the number of hidden nodes or a model mass parameter. We verify these ideas in the scalar field case, where the target distribution is known, and explore implications for cases where it is not known using the MNIST dataset. We also demonstrate that infrared modes are learnt quickest. Journal Article Physical Review D 109 3 American Physical Society (APS) 2470-0010 2470-0029 29 2 2024 2024-02-29 10.1103/physrevd.109.034521 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University SU Library paid the OA fee (TA Institutional Deal) SCOAP3 2024-04-25T21:28:29.1629711 2024-03-04T13:55:21.1988538 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Gert Aarts 0000-0002-6038-3782 1 Biagio Lucini 0000-0001-8974-8266 2 Chanju Park 3 65735__30161__378cce2ee09c45bfa8bf703c346314ff.pdf 65735.VoR.pdf 2024-04-25T21:27:11.7997755 Output 12619048 application/pdf Version of Record true Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. true eng https://creativecommons.org/licenses/by/4.0/
title Scalar field restricted Boltzmann machine as an ultraviolet regulator
spellingShingle Scalar field restricted Boltzmann machine as an ultraviolet regulator
Gert Aarts
Biagio Lucini
Chanju Park
title_short Scalar field restricted Boltzmann machine as an ultraviolet regulator
title_full Scalar field restricted Boltzmann machine as an ultraviolet regulator
title_fullStr Scalar field restricted Boltzmann machine as an ultraviolet regulator
title_full_unstemmed Scalar field restricted Boltzmann machine as an ultraviolet regulator
title_sort Scalar field restricted Boltzmann machine as an ultraviolet regulator
author_id_str_mv 1ba0dad382dfe18348ec32fc65f3f3de
7e6fcfe060e07a351090e2a8aba363cf
60c7e702548bc829b5cbe3040ac41e8e
author_id_fullname_str_mv 1ba0dad382dfe18348ec32fc65f3f3de_***_Gert Aarts
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
60c7e702548bc829b5cbe3040ac41e8e_***_Chanju Park
author Gert Aarts
Biagio Lucini
Chanju Park
author2 Gert Aarts
Biagio Lucini
Chanju Park
format Journal article
container_title Physical Review D
container_volume 109
container_issue 3
publishDate 2024
institution Swansea University
issn 2470-0010
2470-0029
doi_str_mv 10.1103/physrevd.109.034521
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 Restricted Boltzmann machines (RBMs) are well-known tools used in machine learning to learn probability distribution functions from data. We analyze RBMs with scalar fields on the nodes from the perspective of lattice field theory. Starting with the simplest case of Gaussian fields, we show that the RBM acts as an ultraviolet regulator, with the cutoff determined by either the number of hidden nodes or a model mass parameter. We verify these ideas in the scalar field case, where the target distribution is known, and explore implications for cases where it is not known using the MNIST dataset. We also demonstrate that infrared modes are learnt quickest.
published_date 2024-02-29T21:28:29Z
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score 11.016235

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