Invariant Atoms: Sparse Coordinates of Local Semantic Geometry in Language Model Representations
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Semantic-preserving transformations can induce substantial motion in learned representations, while small changes may strongly affect model predictions, raising a basic question: what local metric bes...
arXiv:2607. 26984v1 Announce Type: cross Abstract: Mapping an atomic structure to a compact set of geometric descriptors is an essential step in any machine-learning application to atomic-scale modeling.
arXiv:2609.36458v1 Announce Type: new Abstract: Semantic-preserving transformations can induce substantial motion in learned representations, while small changes may strongly affect model predictions...
arXiv:2606. 12113v1 Announce Type: cross Abstract: Transformer-based language models for SMILES strings suffer from a locality gap: standard character-level tokenization fragments chemically meaningful motifs, forcing models to repeatedly learn local syntax at the expense of long-range dependencies.
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.
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.