“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 17757
School of Mathematics
  Title:   Machine learning parameter systems, Noether normalisations and quasi-stable positions
  Author(s):  Amir Hashemi (Joint with M. Mirhashemi and W. M. Seiler)
  Status:   Published
  Journal: Journal of Symbolic Computation
  Vol.:  126
  Year:  2025
  Pages:   #102345
  Supported by:  IPM
We discuss the use of machine learning models for finding â??good coordinatesâ?� 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.

Download TeX format
back to top
scroll left or right