Journal article 593 views 49 downloads
Quantum field theories, Markov random fields and machine learning
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Biagio Lucini
Journal of Physics: Conference Series, Volume: 2207, Issue: 1, Start page: 012056
Swansea University Authors:
Dimitrios Bachtis, Gert Aarts , Biagio Lucini
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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...
| Published in: | Journal of Physics: Conference Series |
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| ISSN: | 1742-6588 1742-6596 |
| Published: |
IOP Publishing
2022
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| Online Access: |
Check full text
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| 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. |
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| 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 |