arXiv Machine Learning
Jul 1

Symmetry in language statistics shapes the geometry of model representations

arXiv:2602. 15029v3 Announce Type: replace Abstract: The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes can be decoded using a linear probe.

By Dhruva Karkada, Daniel J. Korchinski, Andres Nava, Matthieu Wyart, Yasaman Bahri
arXiv Machine Learning
Sep 11

The information geometry of large language models is shared, learned, and controllable

The paper investigates how large language models (LLMs) share a common Fisher‑Rao geometry in their next‑token probability distributions, revealing that behaviour largely determines this geometry while activation geometry depends on coordinate choices. Across transformer, state‑space, and recurrent architectures, output geometries align more closely than activation geometries, and this shared structure facilitates semantic‑category transfer and improves agreement with human word choices as models scale and train. The study further demonstrates that geometry can guide minimum‑disturbance interventions, enabling reusable control that preserves behaviour better than Euclidean methods and enhances steering, editing, attribution, dictionary learning, and fine‑tuning.

By Dario Picozzi