Quantum field theories, Markov random fields and machine learning
- URL: http://arxiv.org/abs/2110.10928v1
- Date: Thu, 21 Oct 2021 06:50:33 GMT
- Title: Quantum field theories, Markov random fields and machine learning
- Authors: Dimitrios Bachtis, Gert Aarts, Biagio Lucini
- Abstract summary: We will discuss how discretized Euclidean field theories can be recast within the mathematical framework of Markov random fields.
Specifically, we will demonstrate that the $phi4$ scalar field theory on a square lattice satisfies the Hammersley-Clifford theorem.
We will then discuss applications pertinent to the minimization of an asymmetric distance between the probability distribution of the $phi4$ machine learning algorithms and that of target probability distributions.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 from the perspective of quantum
field theory. Here, we will discuss how discretized Euclidean field theories
can be recast within the mathematical framework of Markov random fields, which
is a notable class of probabilistic graphical models with applications in a
variety of research areas, including machine learning. Specifically, we will
demonstrate that the $\phi^{4}$ scalar field theory on a square lattice
satisfies the Hammersley-Clifford theorem, therefore recasting it as a Markov
random field from which neural networks are additionally derived. We will then
discuss applications pertinent to the minimization of an asymmetric distance
between the probability distribution of the $\phi^{4}$ machine learning
algorithms and that of target probability distributions.
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