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Whereas emphasis has been put on training methodologies, less attention has been devoted to particular <jats:italic>model classes<\/jats:italic>: 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 <jats:italic>polynomial circuits<\/jats:italic> 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.<\/jats:p>","DOI":"10.1007\/978-3-031-09843-7_5","type":"book-chapter","created":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T18:04:44Z","timestamp":1656612284000},"page":"77-93","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Categories of\u00a0Differentiable Polynomial Circuits for\u00a0Machine Learning"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3575-135X","authenticated-orcid":false,"given":"Paul","family":"Wilson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6457-1345","authenticated-orcid":false,"given":"Fabio","family":"Zanasi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,6,26]]},"reference":[{"key":"5_CR1","unstructured":"Abadi, M., et al.: TensorFlow: large-scale machine learning on heterogeneous systems (2015). https:\/\/www.tensorflow.org\/"},{"key":"5_CR2","unstructured":"Alarc\u00f3n, F., Anderson, D.: Commutative semirings and their lattices of ideals. 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