mini-vec2vec aligns embedding models with a cheap orthogonal map

measured in 1 paper

Dar replaces vec2vec's adversarial unpaired embedding translation with a three-stage linear pipeline: k-means cluster-landmark matching, Quadratic-Assignment-Problem permutation solving, and ICP-style orthogonal Procrustes refinement [dar-2025-mini-vec2vec-linear-universal-geometry-alignment] Evaluated on the four text encoders vec2vec used (gtr, e5, stella, granite) over the 12 directed pairs, it matches or exceeds vec2vec's top-1 accuracy and average rank on nearly every pair [dar-2025-mini-vec2vec-linear-universal-geometry-alignment] It never collapses on the pairs where adversarial vec2vec was weakest, runs in under 10 minutes on CPU versus 1-7 GPU-days, and shows <=0.01 run-to-run standard deviation [dar-2025-mini-vec2vec-linear-universal-geometry-alignment] This reduces vec2vec's implicit geometric claim to a literal distance-preserving orthogonal rotation between two embedding geometries, recoverable without paired data [dar-2025-mini-vec2vec-linear-universal-geometry-alignment]

Structure

Platonic Representation Hypothesis, Linear Subspace

Context

unsupervised orthogonal Procrustes alignment via cluster-landmark (relative-representation) matching, replacing paired-data supervision, Quadratic Assignment Problem (QAP) permutation solving to match cluster centroids across unpaired embedding spaces, Iterative-Closest-Point-style refinement converging to a stationary orthogonal transformation, direct empirical reduction of vec2vec's adversarial+Gram-matrix-preservation translation to a single linear (orthogonal) map, orders-of-magnitude efficiency and stability improvement over adversarial cross-model alignment, with no collapse on vec2vec's worst-performing pairs

Confirmed in models

GTR-base · GTR (Generalizable T5-based dense Retriever), E5-base-v2 · E5, Stella-base-en-v2 · Stella, Granite-Embedding-278M-Multilingual · Granite Embedding

Method

Orthogonal Procrustes alignment

Papers

mini-vec2vec: Scaling Universal Geometry Alignment with Linear Transformations — Dar, Guy2025 · arXiv:2510.02348