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Quantum field-theoretic machine learning

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

Physical Review D, Volume: 103, Issue: 7

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

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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...

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Published in: Physical Review D
ISSN: 2470-0010 2470-0029
Published: American Physical Society (APS) 2021
Online Access: Check full text

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.
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