Analogical relations fit a rotational operator better than an additive offset

Freenor & Alvarez test whether analogical relations (king-queen, walk-walked) are better modeled as an additive offset or a rotational operator [freenor-alvarez-2025-geometric-rotation-embedding-space] Rotor-invariant shift estimation fits a best-approximating rotation and measures residual invariance across many real word pairs [freenor-alvarez-2025-geometric-rotation-embedding-space] The rotational model achieves lower, more consistent residual error than the additive-offset model across text-embedding-3-large, BGE-M3, and multilingual BERT [freenor-alvarez-2025-geometric-rotation-embedding-space] This is a quantified comparative geometric claim on real embeddings; no causal intervention is performed [freenor-alvarez-2025-geometric-rotation-embedding-space]