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

Dorian Florescu, Matthew England

Research Centre for Computational Science and Mathematical Modelling

University of Bath

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

1 Citation (Scopus)

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
Subtitle of host publication	8th International Conference, Durham, UK, July 22–25, 2024, Proceedings
Editors	Kevin Buzzard, Alicia Dickenstein, Bettina Eick, Anton Leykin, Yue Ren
Publisher	Springer
Pages	186-195
Number of pages	10
Edition	1
ISBN (Electronic)	978-3-031-64529-7
ISBN (Print)	978-3-031-64528-0
DOIs	https://doi.org/10.1007/978-3-031-64529-7_19
Publication status	Published - 17 Jul 2024
Event	International Congress on Mathematical Software 2024 - Durham, United Kingdom Duration: 22 Jul 2024 → 25 Jul 2024 https://maths.dur.ac.uk/icms2024/ICMS2024.html

Publication series

Name	Lecture Notes in Computer Science
Volume	14749
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Congress on Mathematical Software 2024
Country/Territory	United Kingdom
City	Durham
Period	22/07/24 → 25/07/24
Internet address	https://maths.dur.ac.uk/icms2024/ICMS2024.html

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, EP/T015748/1

Keywords

computer algebra
cylindrical algebraic decomposition
machine learning
explainable AI
interpretability
XAI

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, Durham, UK, July 22–25, 2024, Proceedings (1 ed., pp. 186-195). (Lecture Notes in Computer Science; Vol. 14749). Springer . 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, Durham, UK, July 22–25, 2024, Proceedings. ed. / Kevin Buzzard; Alicia Dickenstein; Bettina Eick; Anton Leykin; Yue Ren. 1. ed. Springer , 2024. p. 186-195 (Lecture Notes in Computer Science; Vol. 14749).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

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, Durham, UK, July 22–25, 2024, Proceedings. 1 edn, Lecture Notes in Computer Science, vol. 14749, Springer , pp. 186-195, International Congress on Mathematical Software 2024, Durham, 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, Durham, UK, July 22–25, 2024, Proceedings. 1 ed. Springer . 2024. p. 186-195. (Lecture Notes in Computer Science). Epub 2024 Jul 16. 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, Durham, UK, July 22–25, 2024, Proceedings. editor / Kevin Buzzard ; Alicia Dickenstein ; Bettina Eick ; Anton Leykin ; Yue Ren. 1. ed. Springer , 2024. pp. 186-195 (Lecture Notes in Computer Science).

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

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