arXiv:2607. 04525v1 Announce Type: cross Abstract: How concepts are represented in neural networks is a fundamental question in machine learning.
By Zhimin Hu, Lanhao Niu, Sashank Varma
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:2607. 10578v1 Announce Type: new Abstract: Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge.
By Chunwei Ma, Russell Wolfinger
The paper studies how transformer representations evolve across layers by examining the intrinsic dimensionality (ID) of token embeddings and their neighborhood structures. It finds that closed‑class tokens expand and collapse earlier than open‑class tokens, and that these changes are linked to shifts in local geometry. The authors compare encoder and decoder models, showing distinct layer‑wise behaviors, and demonstrate that geometric features alone can predict a token’s part‑of‑speech and reveal how semantic content changes across layers.
By Samuele Vallisa, Federico Ravenda, Claudio Palominos, Rui He, Andrea Raballo, Antonietta Mira, Philipp Homan, Wolfram Hinzen
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
arXiv:2609.24821v1 Announce Type: new
Abstract: The Linear Representation Hypothesis associates high-level concepts with directions in language models, but it remains unclear how these concept-relate...
By Manjiang Yu, Hongji Li, Zihan Wang, Junwei Chen, Xue Li, Priyanka Singh, Yang Cao, Lijie Hu