תוכניות OT אופטימליות לפי קבוצה ותוצאות להתאמה זרימה

תקציר מקורי באנגליתarXiv:2605.12174v2 Announce Type: replace Abstract: Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce numerical integration cost. Yet, the population-level coupling induced by repeated minibatch OT remains only partially understood. We formalize this coupling as the expected batch OT plan $\overline{\pi}_{k}$, obtained by averaging empirical OT plans over independent minibatches of size $k$. We then establish its large-batch consistency and, in the semidiscrete case relevant to generative modeling, derive rates for both the transport-cost bias and the convergence of $\overline{\pi}_{k}$ to the OT plan. For