Geographic coordinates fit a spherical, not flat, manifold
measured in 1 paperTiblias et al. revisit geographic-location decoding and use sMDS to grid-search candidate curvatures (sphere, cylinder, geodesic great-circle embedding) for city latitude/longitude [tiblias-etal-2025] The spherical manifold achieves the lowest stress across all three models tested, with the recovered projection clustering cities by continent in correct relative real-world position [tiblias-etal-2025] This is a competing curvature claim about the same phenomenon Gurnee & Tegmark decoded from a flat plane, kept separate since the two disagree on curvature rather than domain or mechanism [tiblias-etal-2025]
Structure
Context
space, geography, world models, curvature, geography representation debate
Confirmed in models
Papers
Shape Happens: Automatic Feature Manifold Discovery in LLMs via Supervised Multi-Dimensional Scaling — Tiblias, F., Bigoulaeva, I., Niu, J., Balloccu, S., Gurevych, I.