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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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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
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa60429
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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 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.
College: Faculty of Science and Engineering
Funders: ERC, STFC. Leverhulme Foundation, Royal Society, ERDF (Welsh Government) 813942, WM170010 , RF-2020-461\9, ST/T000813/1
Issue: 1
Start Page: 012056