Machine Learning for Mathematical Software

Matthew England

doi:10.1007/978-3-319-96418-8_20

Machine Learning for Mathematical Software

Matthew England

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

11 Citations (Scopus)

52 Downloads (Pure)

Abstract

While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the author’s own work and similar applications for other mathematical software.

It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.

Original language	English
Title of host publication	Mathematical Software
Subtitle of host publication	Proceedings of the International Congress on Mathematical Software (ICMS 2018)
Editors	J.H. Davenport, M. Kauers, G. Labahn, J. Urban
Publisher	Springer
Pages	165-174
Number of pages	10
ISBN (Electronic)	978-3-319-96418-8
ISBN (Print)	978-3-319-96417-1
DOIs	https://doi.org/10.1007/978-3-319-96418-8_20
Publication status	Published - 14 Jul 2018
Event	International Congress on Mathematical Software: ICMS 2018 - University of Notre Dame, South Bend, United States Duration: 24 Jul 2018 → 27 Jul 2018 Conference number: 6 http://icms-conference.org/2018/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	10931

Conference

Conference	International Congress on Mathematical Software
Abbreviated title	ICMS 2018
Country/Territory	United States
City	South Bend
Period	24/07/18 → 27/07/18
Internet address	http://icms-conference.org/2018/

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-96418-8_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)
ISSN 0302-9743

Keywords

Machine Learning
Mathematical Software

Access to Document

10.1007/978-3-319-96418-8_20

Post-PrintAccepted author manuscript, 698 KB

Cite this

Machine Learning for Mathematical Software. / England, Matthew.
Mathematical Software : Proceedings of the International Congress on Mathematical Software (ICMS 2018). ed. / J.H. Davenport; M. Kauers; G. Labahn; J. Urban. Springer, 2018. p. 165-174 (Lecture Notes in Computer Science; Vol. 10931).

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

England, M 2018, Machine Learning for Mathematical Software. in JH Davenport, M Kauers, G Labahn & J Urban (eds), Mathematical Software : Proceedings of the International Congress on Mathematical Software (ICMS 2018). Lecture Notes in Computer Science, vol. 10931, Springer, pp. 165-174, International Congress on Mathematical Software, South Bend, Indiana, United States, 24/07/18. https://doi.org/10.1007/978-3-319-96418-8_20

@inproceedings{23c06e6c46124b99beb1568284d387d3,

title = "Machine Learning for Mathematical Software",

abstract = "While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the author{\textquoteright}s own work and similar applications for other mathematical software.It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.",

keywords = "Machine Learning, Mathematical Software",

author = "Matthew England",

note = "The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-96418-8_20 Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931) ISSN 0302-9743 ; International Congress on Mathematical Software : ICMS 2018, ICMS 2018 ; Conference date: 24-07-2018 Through 27-07-2018",

year = "2018",

month = jul,

day = "14",

doi = "10.1007/978-3-319-96418-8_20",

language = "English",

isbn = "978-3-319-96417-1",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "165--174",

editor = "J.H. Davenport and M. Kauers and G. Labahn and J. Urban",

booktitle = "Mathematical Software",

address = "United Kingdom",

url = "http://icms-conference.org/2018/",

}

TY - GEN

T1 - Machine Learning for Mathematical Software

AU - England, Matthew

N1 - Conference code: 6

PY - 2018/7/14

Y1 - 2018/7/14

N2 - While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the author’s own work and similar applications for other mathematical software.It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.

AB - While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the author’s own work and similar applications for other mathematical software.It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.

KW - Machine Learning

KW - Mathematical Software

U2 - 10.1007/978-3-319-96418-8_20

DO - 10.1007/978-3-319-96418-8_20

M3 - Conference proceeding

SN - 978-3-319-96417-1

T3 - Lecture Notes in Computer Science

SP - 165

EP - 174

BT - Mathematical Software

A2 - Davenport, J.H.

A2 - Kauers, M.

A2 - Labahn, G.

A2 - Urban, J.

PB - Springer

T2 - International Congress on Mathematical Software

Y2 - 24 July 2018 through 27 July 2018

ER -

Machine Learning for Mathematical Software

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this