Exploring mathematical structure in language may offer valuable insights into questions surrounding large language models. In this talk, we propose that enriched category theory can provide a natural framework for investigating the passage from texts, and probability distributions on them, to a more semantically meaningful space. Motivated by analogies between linear algebra and category theory, we will define a category of expressions in language enriched over the unit interval and then pass to a certain class of functions on those expressions. As we will see, the latter setting has rich mathematical structure and comes with ready-made tools in which to explore that structure.
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