Incremental Monoidal Grammars
This work provides a theoretical foundation for connecting categorical approaches to natural language with machine learning models, but it appears incremental as it builds on existing categorical and grammatical frameworks.
The paper tackles the problem of linking categorical formal grammars to probabilistic language models by defining formal grammars in terms of free monoidal categories and extending this to weighted versions using semirings.
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our construction to weighted formal grammars and weighted automata. This allows us to link the categorical viewpoint on natural language to the standard machine learning notion of probabilistic language model.