Sky sphere representation in language models

We analyze whether language models of size 100B have a representation of the night sky map that is decodable from their residual stream. We find that most of the considered open-source models do have such a representation, and it often even surfaces to the top principal components on prompts that ask questions like ``what is close to this object in the night sky''. In all but one model this representation showed significant scores in LOO testing, containing up to 65-85% of variance (R^2-score) and having median angular error down to 12^\circ-21^\circ. We verify that our representation is not a simple leak from a correlated flat representation. To our knowledge, this representation is the first example of a curved high-dimensional irreducible feature manifold. Codes used in the paper are published at https://github.com/l3erdnik/Decodable-sky