Categories of Differentiable Polynomial Circuits for Machine Learning
Machine Learning
2022-05-10 v2 Category Theory
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.
Cite
@article{arxiv.2203.06430,
title = {Categories of Differentiable Polynomial Circuits for Machine Learning},
author = {Paul Wilson and Fabio Zanasi},
journal= {arXiv preprint arXiv:2203.06430},
year = {2022}
}