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This research demonstrates that large language models can encode complex, non-Euclidean geometric structures like the celestial sphere directly within their residual streams without explicit training on astronomical data. The study confirms these representations are robust and decodable via principal component analysis, marking a significant step toward understanding how LLMs internalize high-dimensional feature manifolds beyond simple linear correlations.
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Sky sphere representation in language models

arXiv2 min read

arXiv:2607.27092v1 Announce Type: new Abstract: 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

Abstract: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 this https URL

Machine Learning (cs.LG)

arXiv:2607.27092 [cs.LG]

(or arXiv:2607.27092v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.27092 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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