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.

Language model prompt optimization research has shown that semantically and grammatically well-formed manually crafted prompts are routinely outperformed by automatically generated token sequences with no apparent meaning or syntactic structure, including sequences of vectors from a model’s embedding space. We use machine-generated prompts to probe how models respond to input that is not composed of natural language expressions. We study the behavior of models of different sizes in multiple semantic tasks in response to both continuous and discrete machine-generated prompts, and compare it to the behavior in response to human-generated natural-language prompts. Even when producing a similar output, machine-generated and human prompts trigger different response patterns through the network processing pathways, including different perplexities, different attention and output entropy distributions, and different unit activation profiles. We provide preliminary insight into the nature of the units activated by different prompt types, suggesting that only natural language prompts recruit a genuinely linguistic circuit.