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Scalar field Restricted Boltzmann Machine as an ultraviolet regulator

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arxiv 2309.15002 v2 pith:ZHQHAX4S submitted 2023-09-26 hep-lat cond-mat.dis-nn

Gert Aarts , Biagio Lucini , Chanju Park This is my paper · ORCID
classification hep-latcond-mat.dis-nn
keywords fieldscalarboltzmanncasedatadistributionfieldsknown
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Restricted Boltzmann Machines (RBMs) are well-known tools used in Machine Learning to learn probability distribution functions from data. We analyse RBMs with scalar fields on the nodes from the perspective of lattice field theory. Starting with the simplest case of Gaussian fields, we show that the RBM acts as an ultraviolet regulator, with the cutoff determined by either the number of hidden nodes or a model mass parameter. We verify these ideas in the scalar field case, where the target distribution is known, and explore implications for cases where it is not known using the MNIST data set. We also demonstrate that infrared modes are learnt quickest.

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Cited by 2 Pith papers

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    SGD weight-matrix eigenvalue fluctuations follow random matrix predictions, with variance proportional to learning rate divided by batch size, the linear scaling rule.

  2. Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics

    hep-lat 2025-01 unverdicted novelty 1.0 of 10

    A perspective article reviewing physics-driven machine learning for inverse problems in QCD, without introducing new data, derivations, or quantitative results.

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