Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

Abstract

There has been recent interest in the use of machine learning (ML) approaches within mathematical software to make choices that impact on the computing performance without affecting the mathematical correctness of the result. We address the problem of selecting the variable ordering for cylindrical algebraic decomposition (CAD), an important algorithm in Symbolic Computation. Prior work to apply ML on this problem implemented a Support Vector Machine (SVM) to select between three existing human-made heuristics, which did better than anyone heuristic alone. The present work extends to have ML select the variable ordering directly, and to try a wider variety of ML techniques.
We experimented with the NLSAT dataset and the Regular Chains Library CAD function for Maple 2018. For each problem, the variable ordering leading to the shortest computing time was selected as the target class for ML. Features were generated from the polynomial input and used to train the following ML models: k-nearest neighbours (KNN) classifier, multi-layer perceptron (MLP), decision tree (DT) and SVM, as implemented in the Python scikit-learn package. We also compared these with the two leading human constructed heuristics for the problem: Brown's heuristic and sotd. On this dataset all of the ML approaches outperformed the human made heuristics, some by a large margin.
LanguageEnglish
Title of host publicationIntelligent Computer Mathematics (Proc. CICM 2019)
Pages(In-press)
Number of pages16
Volume11617
Publication statusAccepted/In press - 24 Apr 2019
Event12th Conference on Intelligent Computer Mathematics - Prague, Czech Republic
Duration: 8 Jul 201912 Jul 2019
Conference number: 12th
https://www.cicm-conference.org/2019/cicm.php

Publication series

NameLecture Notes in Artificial Intelligence

Conference

Conference12th Conference on Intelligent Computer Mathematics
Abbreviated titleCICM 2019
CountryCzech Republic
CityPrague
Period8/07/1912/07/19
Internet address

Fingerprint

Learning systems
Decomposition
Support vector machines
Multilayer neural networks
Decision trees
Classifiers
Polynomials

Keywords

  • computer algebra
  • symbolic computation
  • non-linear real arithmetic
  • cylindrical algebraic decomposition
  • machine learning

Cite this

England, M., & Florescu, D. (Accepted/In press). Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition. In Intelligent Computer Mathematics (Proc. CICM 2019) (Vol. 11617, pp. (In-press)). (Lecture Notes in Artificial Intelligence).

Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition. / England, Matthew; Florescu, Dorian.

Intelligent Computer Mathematics (Proc. CICM 2019). Vol. 11617 2019. p. (In-press) (Lecture Notes in Artificial Intelligence).

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

England, M & Florescu, D 2019, Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition. in Intelligent Computer Mathematics (Proc. CICM 2019). vol. 11617, Lecture Notes in Artificial Intelligence, pp. (In-press), 12th Conference on Intelligent Computer Mathematics, Prague, Czech Republic, 8/07/19.
England M, Florescu D. Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition. In Intelligent Computer Mathematics (Proc. CICM 2019). Vol. 11617. 2019. p. (In-press). (Lecture Notes in Artificial Intelligence).
England, Matthew ; Florescu, Dorian. / Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition. Intelligent Computer Mathematics (Proc. CICM 2019). Vol. 11617 2019. pp. (In-press) (Lecture Notes in Artificial Intelligence).
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