Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.12174 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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 $\overlineπ_{k}$, 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 $\overlineπ_{k}$ to the OT plan. For FM, this yields a population coupling whose induced velocity field is regular enough to define a unique flow from the source to the discrete target. We finally quantify how OT batch size interacts with numerical integration in a tractable two-atom model and in synthetic and image experiments.