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2021

Quantum field theories, Markov random fields and machine learning

Bachtis, Dimitrios, Aarts, Gert, Lucini, Biagio

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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 $\phi^{4}$ 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 $\phi^{4}$ machine learning algorithms and other probability distributions.

Quantum field theories, Markov random fields and machine learning · Around

Built on

E. Nelson, Construction of quantum fields from Markoff fields , Journal of Functional Analysis 12
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A. Milchev, D. W. Heermann and K. Binder, Finite-size scaling analysis of the ϕ 4 \phi^{4} field theory on the square lattice , J. Stat. Phys. 44
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G. Hinton, Training products of experts by minimizing contrastive divergence , Neural Computation, 14
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A. Fischer and C. Igel, Training restricted Boltzmann machines: An introduction , Pattern Recognition 47
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D. Bachtis, G. Aarts and B. Lucini, Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration , Phys. Rev. Research 3
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Original
2021
Closest in time.

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