Analogy parallelograms emerge from Kronecker eigenvector structure
measured in 1 paper- When words are generated by d independent binary semantic attributes, the normalized co-occurrence matrix factorizes as a Kronecker product whose eigenvectors are tensor products of per-attribute vectors. [korchinski-etal-2025-linear-analogies] - Embedding coordinates then become linear (+/-) in the attributes, so parallelogram relations (king - man + woman ≈ queen) emerge exactly, most cleanly for the PMI matrix log M where linearity is independent of signal strength. [korchinski-etal-2025-linear-analogies] - Shown by eigendecomposing a Wikipedia co-occurrence / PMI matrix (10,000-word vocab), reaching ~95% Mikolov-analogy accuracy saturating at rank K=8, plus a synthetic binary-attribute model (100% at K>=d); structure survives removing 85% of the vocabulary. [korchinski-etal-2025-linear-analogies] - The analyzed object is a co-occurrence/PMI matrix, not a trained neural embedding; a single 2025 source with no independent replication. [korchinski-etal-2025-linear-analogies]