• Open access
• Published: 18 January 2024

• Volume 32, article number 4, (2024)
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Applied Categorical Structures

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• Iolo Jones, 
• Jerry Swan & 
• Jeffrey Giansiracusa 

• 83 Accesses
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Abstract

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.

Algebraic Dynamical Systems in Machine LearningOpen accessPublished: 18 January 2024Volume 32, article number 4, (2024)Cite this articleDownload PDFYou have full access to thisopen accessarticleApplied Categorical StructuresAims and scopeSubmit manuscriptAlgebraic Dynamical Systems in Machine LearningDownload PDFIolo Jones, Jerry Swan & Jeffrey Giansiracusa 83 AccessesExplore all metrics AbstractWe 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.

Algebraic Dynamical Systems in Machine Learning | Applied Categorical Structures

https://link.springer.com/article/10.1007/s10485-023-09762-9