Riemannian Geometry for Pre-trained Language Model Embeddings

Abstract:Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety. We ask whether sentence-level classification signal lives in the Riemannian geometry of contextual token embeddings, and probe it by extracting per-token pullback metrics from a learned encoder's analytical Jacobian and aggregating them with the Fréchet mean on the symmetric positive definite (SPD) manifold; we call this procedure Riemannian Mean Pooling (RMP). Across three datasets with non-trivial linguistic structure (CoLA, CREAK, RTE), RMP outperforms Euclidean mean pooling, while on FEVER-Symmetric, a benchmark constructed to remove annotation-driven lexical artifacts, the method correctly stays at chance. Ablations show that a randomly initialised encoder combined with Fréchet aggregation already beats Euclidean pooling on two of the three signal-bearing datasets, localising the source of the gain to the geometric aggregation rather than to learned manifold structure; the trained encoder contributes additional signal specifically on CREAK, the most knowledge-heavy of the three signal-bearing datasets.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI)

arXiv:2607.07047 [cs.CL]

(or arXiv:2607.07047v3 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2607.07047 Focus to learn more arXiv-issued DOI via DataCite

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