arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
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The paper investigates why token prediction, a common pre‑training objective for language models, yields useful representations. It introduces a statistical framework linking token prediction accuracy to the geometry of token embeddings, showing that accurate predictions organize embeddings according to Hellinger distances between context distributions. The authors also propose a self‑consistency principle that refines contextual representations through repeated application of a shared block, and provide downstream guarantees for token generation, community recovery, and linear classification.
arXiv:2609.10305v1 Announce Type: new Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transfor...
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.
Neural Collapse predicts that balanced one-hot classification pushes model representations to be equally far from each other; a symmetric configuration that depends only on the output label and ignores any semantic similarity in the inputs. This creates a puzzle: next-token prediction language models are trained predominantly (as context length increases) with one-hot labels: the same context is very unlikely to appear twice in training with different labels.
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.
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.