Date
2024-06-25Metadata
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Machine learning parameter systems, Noether normalisations and quasi-stable positions
Abstract
We discuss the use of machine learning models for finding “good coordinates” for polynomial ideals. Our main goal is to put ideals into quasi-stable position, as this generic position shares most properties of the generic initial ideal, but can be deterministically reached and verified. Furthermore, it entails a Noether normalisation and provides us with a system of parameters. Traditional approaches use either random choices which typically destroy all sparsity or rather simple human heuristics which are only moderately successful. Our experiments show that machine learning models provide us here with interesting alternatives that most of the time make nearly optimal choices.
Citation
In: Journal of Symbolic Computation Volume 126 (2024-06-25) eissn:1095-855XSponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-2024070510466,
author={Hashemi, Amir and Mirhashemi, Mahshid and Seiler, Werner M.},
title={Machine learning parameter systems, Noether normalisations and quasi-stable positions},
journal={Journal of Symbolic Computation},
year={2024}
}
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2024-07-05T09:22:39Z 2024-07-05T09:22:39Z 2024-06-25 doi:10.17170/kobra-2024070510466 http://hdl.handle.net/123456789/15897 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ Quasi-stable ideals Noether normalisation Systems of parameters Pommaret bases Machine learning Multi-class classification 510 Machine learning parameter systems, Noether normalisations and quasi-stable positions Aufsatz We discuss the use of machine learning models for finding “good coordinates” for polynomial ideals. Our main goal is to put ideals into quasi-stable position, as this generic position shares most properties of the generic initial ideal, but can be deterministically reached and verified. Furthermore, it entails a Noether normalisation and provides us with a system of parameters. Traditional approaches use either random choices which typically destroy all sparsity or rather simple human heuristics which are only moderately successful. Our experiments show that machine learning models provide us here with interesting alternatives that most of the time make nearly optimal choices. open access Hashemi, Amir Mirhashemi, Mahshid Seiler, Werner M. doi:10 .5281 /zenodo .12114165 Maschinelles Lernen Parameteridentifikation Noether-Theorem publishedVersion eissn:1095-855X Journal of Symbolic Computation Volume 126 false Article 102345
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