TH Informal Lattice Meeting

Quantum field-theoretic machine learning and the inverse renormalization group

by Dimitrios Bachtis

online (CERN)




In this talk I will discuss the derivation of machine learning algorithms from quantum field theories and the generation of configurations in absence of the critical slowing down effect via the inverse renormalization group. Based on the Hammersley-Clifford theorem, we will establish an equivalence between lattice field theories and the framework of Markov random fields, hence solidifying a mathematically rigorous connection between the research fields of machine learning, probability theory, statistical mechanics, lattice and constructive field theory. Numerical applications will be additionally discussed. Finally, starting from lattice sizes as small as $V=8^{2}$ in the case of the two-dimensional $\phi^{4}$ theory, we will apply a set of inverse renormalization group transformations to obtain lattice sizes up to $V=512^{2}$, without experiencing the critical slowing down effect. We will then utilize these configurations to calculate two critical exponents. I will conclude by discussing potential future research directions.

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Elena Gianolio
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Ciaran Hughes, Andreas Juttner, Dorota Maria Grabowska, Mattia Dallabrida
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