相关论文: Thermodynamic structure of the Sinkhorn flow

Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…

We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the…

We show that the continuous-time gradient descent in Rn can be viewed as an optimal controlled evolution for a suitable action functional; a similar result holds for stochastic gradient descent. We then provide an analogous characterization…

Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized…

We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show…

We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…

We show that the derivatives of the Sinkhorn-Knopp algorithm, or iterative proportional fitting procedure, converge towards the derivatives of the entropic regularization of the optimal transport problem with a locally uniform linear…

The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…

Optimal transport (OT) and Schr{\"o}dinger bridge (SB) problems have emerged as powerful frameworks for transferring probability distributions with minimal cost. However, existing approaches typically focus on endpoint matching while…

At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…

We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an…

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…

We develop a computationally tractable method for estimating the optimal map between two distributions over $\mathbb{R}^d$ with rigorous finite-sample guarantees. Leveraging an entropic version of Brenier's theorem, we show that our…

We show convergence of the gradients of the Schr\"odinger potentials to the Brenier map in the small-time limit under general assumptions on the marginals, which allow for unbounded densities and supports. Furthermore, we provide novel…

In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations…

Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To…

A computational PDE-constrained optimization approach is proposed for optimal trajectory planning under uncertainty by means of an associated Schroedinger Bridge Problem (SBP). The proposed SBP formulation is interpreted as the mean-field…

Consider the Monge-Kantorovich problem of transporting densities $\rho_0$ to $\rho_1$ on $\mathbb{R}^d$ with a strictly convex cost function. A popular relaxation of the problem is the one-parameter family called the entropic cost problem.…

The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…