Journal article 798 views 129 downloads
Quantum field-theoretic machine learning
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Biagio Lucini
Physical Review D, Volume: 103, Issue: 7
Swansea University Authors:
Dimitrios Bachtis, Gert Aarts , Biagio Lucini
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DOI (Published version): 10.1103/physrevd.103.074510
Abstract
We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the ϕ4 scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as...
| Published in: | Physical Review D |
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| ISSN: | 2470-0010 2470-0029 |
| Published: |
American Physical Society (APS)
2021
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa56753 |
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| Abstract: |
We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the ϕ4 scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the ϕ4 theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the ϕ4 theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory. |
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| Keywords: |
lattice field theory, artificial neural networks, probability theory |
| College: |
Faculty of Science and Engineering |
| Funders: |
The authors received funding from the European
Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme under
grant agreement No. 813942. The work of G. A. and B. L.
has been supported in part by the UKRI Science and
Technology Facilities Council (STFC) Consolidated Grant
No. ST/P00055X/1. The work of B. L. is further supported
in part by the Royal Society Wolfson Research Merit
Award No. WM170010 and by the Leverhulme Foundation
Research Fellowship RF-2020-461\9. Numerical simulations have been performed on the Swansea SUNBIRD
system. This system is part of the Supercomputing Wales
project, which is part-funded by the European Regional
Development Fund (ERDF) via Welsh Government. We
thank European Cooperation in Science and Technology
Action CA15213 THOR for support. |
| Issue: |
7 |