Representations as Language: An Information-Theoretic Framework for Interpretability
Henry Conklin, Kenny Smith
TL;DR
This work addresses the opacity of large transformer representations by proposing an information-theoretic framework that treats the sentence-to-representation mapping as a language. It discretizes latent vectors into symbols and defines four structure measures—$ Information$, $Variation$, $Regularity$, and $Disentanglement$—based on a fast, dimension-wise entropy estimator $H_{dw}$, enabling analysis across tokens, POS, and bigrams. The study reveals two training phases: an initial in-distribution learning phase with increasing regularity and disentanglement, followed by a long phase of robustness-to-noise and representational compression, during which generalisation improves and larger models compress more. These findings illuminate how scale and training dynamics shape representational structure, offering practical insight into predicting generalisation and guiding model design for robust language understanding.
Abstract
Large scale neural models show impressive performance across a wide array of linguistic tasks. Despite this they remain, largely, black-boxes - inducing vector-representations of their input that prove difficult to interpret. This limits our ability to understand what they learn, and when the learn it, or describe what kinds of representations generalise well out of distribution. To address this we introduce a novel approach to interpretability that looks at the mapping a model learns from sentences to representations as a kind of language in its own right. In doing so we introduce a set of information-theoretic measures that quantify how structured a model's representations are with respect to its input, and when during training that structure arises. Our measures are fast to compute, grounded in linguistic theory, and can predict which models will generalise best based on their representations. We use these measures to describe two distinct phases of training a transformer: an initial phase of in-distribution learning which reduces task loss, then a second stage where representations becoming robust to noise. Generalisation performance begins to increase during this second phase, drawing a link between generalisation and robustness to noise. Finally we look at how model size affects the structure of the representational space, showing that larger models ultimately compress their representations more than their smaller counterparts.