Towards Spectroscopy: Susceptibility Clusters in Language Models

Spectroscopy infers the internal structure of physical systems by measuring their response to perturbations. We apply this principle to neural networks: perturbing the data distribution by upweighting a token $y$ in context $x$, we measure the model's response via susceptibilities $\chi_{xy}$, which are covariances between component-level observables and the perturbation computed over a localized Gibbs posterior via stochastic gradient Langevin dynamics (SGLD). Theoretically, we show that susceptibilities decompose as a sum over \emph{modes} of the data distribution, explaining why tokens that follow their contexts ``for similar reasons'' cluster together in susceptibility space. Empirically, we apply this methodology to Pythia-14M, developing a conductance-based clustering algorithm that identifies 510 interpretable clusters ranging from grammatical patterns to code structure to mathematical notation. Comparing to sparse autoencoders, 50\% of our clusters match SAE features, validating that both methods recover similar structure.

We study how a language model understands text by perturbing the weights in a component of the model, and measuring how performance on a specific task (ie predicting a certain word in a given context) changes. We do this for many components and many different tasks, and discover clusters, groups of words and contexts that the model views as similar. We discuss discovered clusters, and what they reveal about how the LLMs in question perceive and function.