Dynamic applications, including optimal-transport Flow Matching, repeatedly solve related entropic optimal transport problems, yet conventional distributed Sinkhorn processes frames sequentially and synchronizes after every iteration. We present TemporalSinkhorn, a parallel-in-time executor that batches future candidates and their repairs without making output accuracy speculative. A centered, row-sharded certificate accepts only a deterministic safe prefix. The remaining candidates share packed Sinkhorn updates; an online projective forgetting rate places audit milestones, while a posteriori residual checks recover from every depth underestimate. Prediction can therefore change work placement but cannot authorize an inaccurate output. On 4 A100 GPUs, a 60-run, five-seed grid at n = 2048 shows that forgetting-guided milestones reduce wall time by 1.15x-1.47x relative to auditing every packed iteration in five statistically resolved regime cells. Against a sequential soft c-transform warm start, temporal execution is 1.42x-3.55x faster across six synthetic streams, with zero marginal-tolerance violations. On Flow Matching minibatch streams, temporal execution is 3.054x-3.632x faster than sequential carry at n = 2048, with no tolerance violations. A separate fixed-kernel test on an RTX 4060 Laptop GPU gives a 4.315x geometric-mean speedup. These are complementary deployment studies rather than a controlled hardware comparison. End-to-end Flow Matching integration, optimized-solver comparisons, and multi-node validation remain open.
Francisco Andrade, Gabriel Peyré, Clarice Poonmath.ST cs.LG
Optimal transport (OT) has become a central language for comparing probability measures, but exact balanced OT is often both too rigid for data with missing, created, or destroyed mass and subject to unfavorable high-dimensional sample complexity. Entropic regularization and unbalanced relaxations address these limitations in complementary ways. Entropy smooths the geometry, improves statistical behavior, and enables fast Sinkhorn-type algorithms, while unbalanced marginal penalties replace hard conservation constraints by divergence terms adapted to noisy empirical data. This paper studies the sample complexity of entropic unbalanced OT at the level of the optimal coupling, rather than only the scalar transport value. We develop a translation-invariant dual formulation, prove compactness and strong convexity properties for the intrinsic dual variables, and convert these geometric estimates into high-probability finite-sample bounds for empirical couplings. The results clarify why regularization is a practical necessity in machine learning applications: it softens the curse of dimensionality, reduces the number of samples needed for stable transport estimation, and keeps the resulting estimators compatible with scalable Sinkhorn-type solvers.