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Main Authors: Gordon, Andrew, Baker, Garrett, Wang, George, Snell, William, van Wingerden, Stan, Murfet, Daniel
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.12703
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author Gordon, Andrew
Baker, Garrett
Wang, George
Snell, William
van Wingerden, Stan
Murfet, Daniel
author_facet Gordon, Andrew
Baker, Garrett
Wang, George
Snell, William
van Wingerden, Stan
Murfet, Daniel
contents 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 $χ_{xy}$, 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 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_12703
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Towards Spectroscopy: Susceptibility Clusters in Language Models
Gordon, Andrew
Baker, Garrett
Wang, George
Snell, William
van Wingerden, Stan
Murfet, Daniel
Machine Learning
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 $χ_{xy}$, 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 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.
title Towards Spectroscopy: Susceptibility Clusters in Language Models
topic Machine Learning
url https://arxiv.org/abs/2601.12703