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Scalar field restricted Boltzmann machine as an ultraviolet regulator
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Biagio Lucini ,
Chanju Park
Physical Review D, Volume: 109, Issue: 3
Swansea University Authors:
Gert Aarts , Biagio Lucini , Chanju Park
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DOI (Published version): 10.1103/physrevd.109.034521
Abstract
Restricted Boltzmann machines (RBMs) are well-known tools used in machine learning to learn probability distribution functions from data. We analyze 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...
| Published in: | Physical Review D |
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| ISSN: | 2470-0010 2470-0029 |
| Published: |
American Physical Society (APS)
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa65735 |
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| Abstract: |
Restricted Boltzmann machines (RBMs) are well-known tools used in machine learning to learn probability distribution functions from data. We analyze 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 dataset. We also demonstrate that infrared modes are learnt quickest. |
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| College: |
Faculty of Science and Engineering |
| Funders: |
SCOAP3 |
| Issue: |
3 |