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Quantum field theories, Markov random fields and machine learning

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

Journal of Physics: Conference Series, Volume: 2207, Issue: 1, Start page: 012056

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

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DOI (Published version): 10.1088/1742-6596/2207/1/012056

Abstract

The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up the opportunity to investigate probabilistic machine learning within quantum field theory. Here, we will discuss how discretized Euclidean field theories, such as the ϕ4 latt...

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Published in: Journal of Physics: Conference Series
ISSN: 1742-6588 1742-6596
Published: IOP Publishing 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa60429
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first_indexed 2022-07-08T19:09:41Z
last_indexed 2023-01-13T19:20:33Z
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spelling v2 60429 2022-07-08 Quantum field theories, Markov random fields and 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 2022-07-08 SPH The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up the opportunity to investigate probabilistic machine learning within quantum field theory. Here, we will discuss how discretized Euclidean field theories, such as the ϕ4 lattice field theory on a square lattice, are mathematically equivalent to Markov fields, a notable class of probabilistic graphical models with applications in a variety of research areas, including machine learning. The results are established based on the Hammersley-Clifford theorem. We will then derive neural networks from quantum field theories and discuss applications pertinent to the minimization of the Kullback-Leibler divergence for the probability distribution of the ϕ4 machine learning algorithms and other probability distributions. Journal Article Journal of Physics: Conference Series 2207 1 012056 IOP Publishing 1742-6588 1742-6596 1 3 2022 2022-03-01 10.1088/1742-6596/2207/1/012056 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University Another institution paid the OA fee ERC, STFC. Leverhulme Foundation, Royal Society, ERDF (Welsh Government) 813942, WM170010 , RF-2020-461\9, ST/T000813/1 813942, WM170010 , RF-2020-461\9, ST/T000813/1 2023-06-23T15:42:16.1536474 2022-07-08T20:04:46.1261301 Faculty of Science and Engineering Dimitrios Bachtis 1 Gert Aarts 0000-0002-6038-3782 2 Biagio Lucini 0000-0001-8974-8266 3 60429__24519__dc201574c4494352b5f9e7d58de300ce.pdf Bachtis_2022_J._Phys.__Conf._Ser._2207_012056.pdf 2022-07-08T20:07:21.4798388 Output 1165075 application/pdf Version of Record true Content from this work may be used under the terms of theCreative Commons Attribution 3.0 licence true eng http://creativecommons.org/licenses/by/3.0
title Quantum field theories, Markov random fields and machine learning
spellingShingle Quantum field theories, Markov random fields and machine learning
Dimitrios Bachtis
Gert Aarts
Biagio Lucini
title_short Quantum field theories, Markov random fields and machine learning
title_full Quantum field theories, Markov random fields and machine learning
title_fullStr Quantum field theories, Markov random fields and machine learning
title_full_unstemmed Quantum field theories, Markov random fields and machine learning
title_sort Quantum field theories, Markov random fields and 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 Journal of Physics: Conference Series
container_volume 2207
container_issue 1
container_start_page 012056
publishDate 2022
institution Swansea University
issn 1742-6588
1742-6596
doi_str_mv 10.1088/1742-6596/2207/1/012056
publisher IOP Publishing
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
document_store_str 1
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description The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up the opportunity to investigate probabilistic machine learning within quantum field theory. Here, we will discuss how discretized Euclidean field theories, such as the ϕ4 lattice field theory on a square lattice, are mathematically equivalent to Markov fields, a notable class of probabilistic graphical models with applications in a variety of research areas, including machine learning. The results are established based on the Hammersley-Clifford theorem. We will then derive neural networks from quantum field theories and discuss applications pertinent to the minimization of the Kullback-Leibler divergence for the probability distribution of the ϕ4 machine learning algorithms and other probability distributions.
published_date 2022-03-01T15:42:11Z
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score 11.037581

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