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arXiv · 2110.10928

Quantum field theories, Markov random fields and machine learning

Dimitrios Bachtis·Gert Aarts·Biagio Lucini
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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 $\phi^{4}$ 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.

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Dimitrios Bachtis, Gert Aarts, Biagio Lucini. 2021-10-21. Quantum field theories, Markov random fields and machine learning. https://doi.org/10.1088/1742-6596%2F2207%2F1%2F012056

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