Scalar field Restricted Boltzmann Machine as an ultraviolet regulator

Fuente: arXiv
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Main Authors: Aarts, Gert, Lucini, Biagio, Park, Chanju
Format: Preprint
Published: 2023
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author Aarts, Gert
Lucini, Biagio
Park, Chanju
author_facet Aarts, Gert
Lucini, Biagio
Park, Chanju
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2309_15002
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Scalar field Restricted Boltzmann Machine as an ultraviolet regulator
Aarts, Gert
Lucini, Biagio
Park, Chanju
High Energy Physics - Lattice
Disordered Systems and Neural Networks
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.
title Scalar field Restricted Boltzmann Machine as an ultraviolet regulator
topic High Energy Physics - Lattice
Disordered Systems and Neural Networks
url https://arxiv.org/abs/2309.15002