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Algebraic Dynamical Systems in Machine Learning

Jones, Iolo; Swan, Jerry; Giansiracusa, Jeffrey

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Iolo Jones
PGR Student Doctor of Philosophy

Jerry Swan


We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures for dynamic machine learning models (including recurrent neural networks, graph neural networks, and diffusion models) can be embedded. Considered in category theory, we also show that these algebraic models are a natural language for describing the compositionality of dynamic models. Furthermore, we propose that these models provide a template for the generalisation of the above dynamic models to learning problems on structured or non-numerical data, including ‘hybrid symbolic-numeric’ models.


Jones, I., Swan, J., & Giansiracusa, J. (2024). Algebraic Dynamical Systems in Machine Learning. Applied Categorical Structures, 32(1), Article 4.

Journal Article Type Article
Acceptance Date Dec 13, 2023
Online Publication Date Jan 18, 2024
Publication Date Feb 1, 2024
Deposit Date Dec 7, 2023
Publicly Available Date Jan 19, 2024
Journal Applied Categorical Structures
Print ISSN 0927-2852
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 32
Issue 1
Article Number 4
Keywords Term rewriting, Functional programming, Machine learning, Compositionality, Dynamical systems
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