Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems

Dorian Florescu; Matthew England

doi:10.1007/978-3-031-64529-7_19

Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems

Coventry University

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Abstract

We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may be represented as a constrained neural network. This allows us to then use machine learning methods to further optimise the heuristic, leading to new networks of similar size, representing new heuristics of similar complexity as the original human-designed one. We present this as a form of ante-hoc explainability for use in computer algebra development.

Original language	English
Title of host publication	Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings
Editors	Kevin Buzzard, Alicia Dickenstein, Bettina Eick, Anton Leykin, Yue Ren
Place of Publication	Cham, Switzerland
Publisher	Springer, Cham
Pages	186-195
Number of pages	10
ISBN (Print)	9783031645280
DOIs	https://doi.org/10.1007/978-3-031-64529-7_19
Publication status	Published - 17 Jul 2024
Event	8th International Conference on Mathematical Software, ICMS 2024 - Durham, UK United Kingdom Duration: 22 Jul 2024 → 25 Jul 2024

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14749 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th International Conference on Mathematical Software, ICMS 2024
Country/Territory	UK United Kingdom
City	Durham
Period	22/07/24 → 25/07/24

Funding

DF and ME were both supported by EPSRC grant EP/R019622/1: Embedding Machine Learning within Quantifier Elimination Procedures. ME was also supported by EPSRC grant EP/T015748/1: Pushing Back the Doubly-Exponential Wall of Cylindrical Algebraic Decomposition (DEWCAD).

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/R019622/1
Embedding Machine Learning	EP/T015748/1

Keywords

computer algebra
cylindrical algebraic decomposition
explainable AI
interpretability
machine learning
XAI

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-64529-7_19

Cite this

Florescu, D., & England, M. (2024). Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems. In K. Buzzard, A. Dickenstein, B. Eick, A. Leykin, & Y. Ren (Eds.), Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings (pp. 186-195). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14749 LNCS). Springer, Cham. https://doi.org/10.1007/978-3-031-64529-7_19

Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems. / Florescu, Dorian; England, Matthew.
Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings. ed. / Kevin Buzzard; Alicia Dickenstein; Bettina Eick; Anton Leykin; Yue Ren. Cham, Switzerland: Springer, Cham, 2024. p. 186-195 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14749 LNCS).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Florescu, D & England, M 2024, Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems. in K Buzzard, A Dickenstein, B Eick, A Leykin & Y Ren (eds), Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14749 LNCS, Springer, Cham, Cham, Switzerland, pp. 186-195, 8th International Conference on Mathematical Software, ICMS 2024, Durham, UK United Kingdom, 22/07/24. https://doi.org/10.1007/978-3-031-64529-7_19

Florescu D, England M. Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems. In Buzzard K, Dickenstein A, Eick B, Leykin A, Ren Y, editors, Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings. Cham, Switzerland: Springer, Cham. 2024. p. 186-195. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-64529-7_19

Florescu, Dorian ; England, Matthew. / Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems. Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings. editor / Kevin Buzzard ; Alicia Dickenstein ; Bettina Eick ; Anton Leykin ; Yue Ren. Cham, Switzerland : Springer, Cham, 2024. pp. 186-195 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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