Large language models transition from integrating across position-yoked, exponential windows to structure-yoked, power-law windows

Modern language models excel at integrating across long temporal scales needed to encode linguistic meaning and show non-trivial similarities to biological neural systems. Prior work suggests that human brain responses to language exhibit hierarchically organized "integration windows" that substantially constrain the overall influence of an input token (e.g., a word) on the neural response. However, little prior work has attempted to use integration windows to characterize computations in large language models (LLMs). We developed a simple word-swap procedure for estimating integration windows from black-box language models that does not depend on access to gradients or knowledge of the model architecture (e.g., attention weights). Using this method, we show that trained LLMs exhibit stereotyped integration windows that are well-fit by a convex combination of an exponential and a power-law function, with a partial transition from exponential to power-law dynamics across network layers. We then introduce a metric for quantifying the extent to which these integration windows vary with structural boundaries (e.g., sentence boundaries), and using this metric, we show that integration windows become increasingly yoked to structure at later network layers. None of these findings were observed in an untrained model, which as expected integrated uniformly across its input. These results suggest that LLMs learn to integrate information in natural language using a stereotyped pattern: integrating across position-yoked, exponential windows at early layers, followed by structure-yoked, power-law windows at later layers. The methods we describe in this paper provide a general-purpose toolkit for understanding temporal integration in language models, facilitating cross-disciplinary research at the intersection of biological and artificial intelligence.