An enriched category theory of language: from syntax to semantics
This work provides a foundational mathematical approach for bridging syntax and semantics in language models, potentially impacting natural language processing and AI by offering a new way to interpret model outputs.
The paper tackles the problem of deriving semantic information from probability distributions on text extensions, as learned by large language models, by proposing a mathematical framework that transforms these distributions into an enriched category containing semantic concepts like entailment and logical operations.
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sophistication, including a knowledge of grammar and semantics. In this paper, we propose a mathematical framework for passing from probability distributions on extensions of given texts, such as the ones learned by today's large language models, to an enriched category containing semantic information. Roughly speaking, we model probability distributions on texts as a category enriched over the unit interval. Objects of this category are expressions in language, and hom objects are conditional probabilities that one expression is an extension of another. This category is syntactical -- it describes what goes with what. Then, via the Yoneda embedding, we pass to the enriched category of unit interval-valued copresheaves on this syntactical category. This category of enriched copresheaves is semantic -- it is where we find meaning, logical operations such as entailment, and the building blocks for more elaborate semantic concepts.