Categories of differentiable polynomial circuits for machine learning
Categories of differentiable polynomial circuits for machine learning
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. 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.
77-93
Wilson, Paul
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Zanasi, Fabio
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Wilson, Paul
dd7e263e-2ef5-4245-b0b2-a8ac5e3923fa
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
Wilson, Paul and Zanasi, Fabio
(2022)
Categories of differentiable polynomial circuits for machine learning.
Behr, Nicholas and Strüber, Daniel
(eds.)
In Graph Transformation: 15th International Conference, ICGT 2022, Held as Part of STAF 2022, Nantes, France, July 7–8, 2022, Proceedings.
Springer Cham.
.
(doi:10.1007/978-3-031-09843-7_5).
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Conference or Workshop Item
(Paper)
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. 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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978-3-031-09843-7_5
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e-pub ahead of print date: 26 June 2022
Venue - Dates:
International Conference on Graph Transformation 2022: The 11th International Colloquium on Graph Theory and combinatorics, , Montpellier, France, 2022-07-04 - 2022-07-08
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Local EPrints ID: 483719
URI: http://eprints.soton.ac.uk/id/eprint/483719
ISSN: 0302-9743
PURE UUID: eadf8421-4105-4b29-828e-d1d691927fac
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Date deposited: 03 Nov 2023 17:59
Last modified: 18 Mar 2024 03:49
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Contributors
Author:
Paul Wilson
Author:
Fabio Zanasi
Editor:
Nicholas Behr
Editor:
Daniel Strüber
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