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Machine learning with quantum field theories

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

Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021), Volume: 396

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

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DOI (Published version): 10.22323/1.396.0201

Abstract

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contri...

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Published in: Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)
ISSN: 1824-8039
Published: Trieste, Italy Sissa Medialab 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa60431
first_indexed 2022-07-08T19:50:02Z
last_indexed 2023-01-13T19:20:33Z
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spelling 2022-07-11T14:48:51.3148718 v2 60431 2022-07-08 Machine learning with quantum field theories 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 BGPS The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the ϕ4 scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the ϕ4 theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the ϕ4 machine learning algorithms and target probability distributions. Conference Paper/Proceeding/Abstract Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) 396 Sissa Medialab Trieste, Italy 1824-8039 8 7 2022 2022-07-08 10.22323/1.396.0201 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University Another institution paid the OA fee ERC, STFC. Leverhulme Foundation, Royal Society, ERDF 813942, WM170010 , RF-2020-461\9, ST/T000813/1 2022-07-11T14:48:51.3148718 2022-07-08T20:47:40.4075075 College of Science College of Science Dimitrios Bachtis 1 Gert Aarts 0000-0002-6038-3782 2 Biagio Lucini 0000-0001-8974-8266 3 60431__24522__27c1d051b3f24a4a8d752afcdc699aa6.pdf LATTICE2021_201.pdf 2022-07-08T20:49:18.7212439 Output 994049 application/pdf Version of Record true © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Machine learning with quantum field theories
spellingShingle Machine learning with quantum field theories
Dimitrios Bachtis
Gert Aarts
Biagio Lucini
title_short Machine learning with quantum field theories
title_full Machine learning with quantum field theories
title_fullStr Machine learning with quantum field theories
title_full_unstemmed Machine learning with quantum field theories
title_sort Machine learning with quantum field theories
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 Conference Paper/Proceeding/Abstract
container_title Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)
container_volume 396
publishDate 2022
institution Swansea University
issn 1824-8039
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publisher Sissa Medialab
college_str College of Science
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hierarchy_parent_title College of Science
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description The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the ϕ4 scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the ϕ4 theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the ϕ4 machine learning algorithms and target probability distributions.
published_date 2022-07-08T20:13:01Z
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