Towards Spectroscopy: Susceptibility Clusters in Language Models

Andrew Gordon, Garrett Baker, George Wang, William Snell, Stan Van Wingerden, Daniel Murfet
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:36247-36314, 2026.

Abstract

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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-gordon26a, title = {Towards Spectroscopy: Susceptibility Clusters in Language Models}, author = {Gordon, Andrew and Baker, Garrett and Wang, George and Snell, William and Van Wingerden, Stan and Murfet, Daniel}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {36247--36314}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/gordon26a/gordon26a.pdf}, url = {https://proceedings.mlr.press/v306/gordon26a.html}, abstract = {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 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.} }
Endnote
%0 Conference Paper %T Towards Spectroscopy: Susceptibility Clusters in Language Models %A Andrew Gordon %A Garrett Baker %A George Wang %A William Snell %A Stan Van Wingerden %A Daniel Murfet %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-gordon26a %I PMLR %P 36247--36314 %U https://proceedings.mlr.press/v306/gordon26a.html %V 306 %X 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 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.
APA
Gordon, A., Baker, G., Wang, G., Snell, W., Van Wingerden, S. & Murfet, D.. (2026). Towards Spectroscopy: Susceptibility Clusters in Language Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:36247-36314 Available from https://proceedings.mlr.press/v306/gordon26a.html.

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