An axiomatic approach to differentiation of polynomial circuits
An axiomatic approach to differentiation of polynomial circuits
Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model class. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.
Wilson, Paul
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Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
October 2023
Wilson, Paul
dd7e263e-2ef5-4245-b0b2-a8ac5e3923fa
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
Wilson, Paul and Zanasi, Fabio
(2023)
An axiomatic approach to differentiation of polynomial circuits.
Journal of Logical and Algebraic Methods in Programming, 135, [100892].
(doi:10.1016/j.jlamp.2023.100892).
Abstract
Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model class. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.
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Accepted/In Press date: 22 June 2023
e-pub ahead of print date: 30 June 2023
Published date: October 2023
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© 2023 The Author(s)
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Local EPrints ID: 484080
URI: http://eprints.soton.ac.uk/id/eprint/484080
ISSN: 2352-2208
PURE UUID: 5b2c3465-3ef0-4f90-9f50-45ce4485c46e
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Date deposited: 09 Nov 2023 18:14
Last modified: 18 Mar 2024 03:49
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Author:
Paul Wilson
Author:
Fabio Zanasi
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