vec2vec-ot-baseline-four-algorithms-hungarian-discrete

IN premise — summaries/2026/08/24/jha-2025-vec2vec-s2-mean-rank-average-rank-position-of-the-correct-embedding-mat.md

Created 2026-08-24T17:10:57+00:00

The oracle-aided optimal transport baseline compares four algorithms—Hungarian (discrete permutation, evaluated only on Top-1 Accuracy), Earth Mover's Distance, Sinkhorn, and Gromov-Wasserstein (entropic and non-entropic variants, multiple hyperparameters)—with continuous methods scored on Top-1, Mean Rank, and Mean Cosine Similarity via barycenter v′ᵢ = (Σⱼ Pᵢⱼ vⱼ) / (Σⱼ Pᵢⱼ).

Summary

This sets up the experimental yardstick for comparing how well four different matching algorithms pair source vectors with target vectors, with the key constraint that the discrete Hungarian method can only be scored on whether it picks the single best match, while the three continuous methods get a richer scorecard that also includes average rank and how closely the weighted blend of their matches aligns geometrically. That asymmetry in scoring means no single number lets you rank all four algorithms head-to-head, so any comparison must account for what each method's output format actually allows you to measure.