Towards Spectroscopy: Susceptibility Clusters in Language Models
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915737878134784 |
|---|---|
| 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 |