Riemannian Geometry for Pre-trained Language Model Embeddings
This work proposes Riemannian Mean Pooling (RMP), which extracts per-token pullback metrics from a learned encoder's analytical Jacobian and aggregates them via Fréchet mean on the SPD manifold. RMP outperforms Euclidean mean pooling on CoLA, CREAK, and RTE, while staying at chance on FEVER-Symmetric. Ablations show that even a randomly initialized encoder with Fréchet aggregation beats Euclidean pooling on most datasets, locating the gain in geometric aggregation.
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[Submitted on 8 Jul 2026]
Title:Riemannian Geometry for Pre-trained Language Model Embeddings
View a PDF of the paper titled Riemannian Geometry for Pre-trained Language Model Embeddings, by Szczepan Konior and Alexandre Quemy and Przemys{\l}aw Klocek and Gr\'egoire Cattan and Bart{\l}omiej Sobieski
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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.
Subjects:
Computation and Language (cs.CL); Artificial Intelligence (cs.AI)
Cite as: arXiv:2607.07047 [cs.CL]
(or arXiv:2607.07047v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2607.07047
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Alexandre Quemy [view email] [v1] Wed, 8 Jul 2026 06:23:46 UTC (421 KB)
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