Categories of Differentiable Polynomial Circuits for Machine Learning

Paul Wilson; Fabio Zanasi

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arXiv · 2203.06430

Categories of Differentiable Polynomial Circuits for Machine Learning

Paul Wilson·Fabio Zanasi

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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 \emph{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 \emph{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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Paul Wilson, Fabio Zanasi. 2022-03-12. Categories of Differentiable Polynomial Circuits for Machine Learning. https://arxiv.org/abs/2203.06430

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