Analysing the Linearity of Linguistic Relations in Language Model Embedding Spaces

Abstract:We propose a framework to analyse how strongly different linguistic relations are linearly encoded in language model embedding spaces. We formalise linear encoding via a constrained linear approximation over related and unrelated word pairs and apply this to an extended BATS dataset covering inflectional, derivational, lexicographic, and encyclopedic relations in GloVe, RoBERTa, and ModernBERT. Our experiments show near-perfect linear encodings for inflectional and derivational relations, but substantially higher errors for lexicographic and encyclopedic relations, especially for one-to-many and many-to-many associations. We also find that RoBERTa and ModernBERT generally encode relations more linearly than GloVe. These results indicate that our framework can reveal which relational structures are most linearly accessible in embeddings, offering a compact tool for probing and comparing relational geometry across models.

6 pages. Accepted at the Workshop on Scientific Methods for Understanding Deep Learning (Sci4DL) at ICLR 2026

Computation and Language (cs.CL); Machine Learning (cs.LG)

arXiv:2609.21655 [cs.CL]

(or arXiv:2609.21655v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2609.21655 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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