For a language model (LM) to faithfully model human language, it must compress vast, potentially infinite information into relatively few dimensions. We propose analyzing compression in (pre-trained) LMs from two points of view: geometric and information-theoretic. We demonstrate that the two views are highly correlated, such that the intrinsic geometric dimension of linguistic data predicts their coding length under the LM. We then show that, in turn, high compression of a linguistic dataset predicts rapid adaptation to that dataset, confirming that being able to compress linguistic information is an important part of successful LM performance. As a practical byproduct of our analysis, we evaluate a battery of intrinsic dimension estimators for the first time on linguistic data, showing that only some encapsulate the relationship between information-theoretic compression, geometric compression, and ease-of-adaptation.

Compositionality is a hallmark of human language that not only enables linguistic generalization, but also potentially facilitates acquisition. When simulating language emergence with neural networks, compositionality has been shown to improve communication performance; however, its impact on imitation learning has yet to be investigated. Our work explores the link between compositionality and imitation in a Lewis game played by deep neural agents. Our contributions are twofold: first, we show that the learning algorithm used to imitate is crucial: supervised learning tends to produce more average languages, while reinforcement learning introduces a selection pressure toward more compositional languages. Second, our study reveals that compositional languages are easier to imitate, which may induce the pressure toward compositional languages in RL imitation settings.