arXiv research

Optimizes angular velocity transfers for rigid bodies under deadline constraints.

Revisits shallow neural networks using Lipschitz norms and measures.

The paper establishes general results in Lorentzian optimal transport theory.

New method calculates cut locus on Riemannian manifolds using optimal transport.

Muon dynamics study uses spectral Wasserstein flow for optimization stability.

This thesis uses Kantorovich-Rubinstein distance for classifying points based on their measures.

To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1 distance. However, it was not clear how cycleGAN-type generative models can be deriv…

New algorithm for linear bandits tackles Optimal Transport problems.

Formula derived for curvature in measure spaces.

This paper studies neural network operators and their convergence properties.

Efficiently predicts optimal transport plans using sliced potentials.

New framework enhances neural network robustness against adversarial attacks.

Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.

Study optimal transport on globally hyperbolic spacetimes, focusing on weak Kantorovich potentials' regularity.

The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein.

We refine and generalize several interpolation inequalities bounding the $L^p$ norm of a probability density with respect to the reference measure $μ$ by its Sobolev norm and the Kantorovich distance to $μ$ on a smooth weighted Riemannian manifold satisfying $CD(0, \infty)$ condition.

New method trains normalizing flows using entropy-regularized transport.

Unified approach solves Kyle model with dynamic information.

Proves uniqueness of barycenters on manifolds without restrictions.

Adapts Stein's method for geometric inequalities, addressing boundary terms.

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of $d$-dimensional histograms having $n$ bins each. We prove that this problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+1)$-partite graph with $(d+1)n$ nodes and $dn^{\frac{d+1}{d}}$ arcs,…

Optimizes risk measures given known marginal distributions of two unknown factors.

Unified framework for analyzing gradient flows of measures with exponential decay of entropy.

A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.

Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.

New framework for optimal transport with jumps over intermediate spaces.

This work develops sampling methods for differential privacy using SHK geometry.

New algorithm for estimating multivariate quantiles using stochastic optimal transport.

Study sharp convergence rates of empirical UOT for spatio-temporal point processes.

This work robustifies Wasserstein distance estimation with MoM estimators for outlier-polluted data.

This paper uses UOT metrics for better dimensionality reduction and classification/clustering.

Generative modelling is often cast as minimizing a similarity measure between a data distribution and a model distribution. Recently, a popular choice for the similarity measure has been the Wasserstein metric, which can be expressed in the Kantorovich duality formulation as the optimum difference of the expected value…

The study analyzes the evolution of Gaussian measures under a specific gradient flow.

Proposes a variational NNCC formulation for infinite dimensions.

A general duality proof for Wasserstein distributionally robust optimization.

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel …

Let $M,N$ be two smooth compact hypersurfaces of $\mathbb{R}^n$ which bound strictly convex domains equipped with two absolutely continuous measures $μ$ and $ν$ (with respect to the volume measures of $M$ and $N$). We consider the optimal transportation from $μ$ to $ν$ for the quadratic cost. Let $(φ:m \to \mathbb{R},ψ…

On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation. These notions also make sense in a (nonsmooth) metric measure setting, where they…

Paper introduces SGA for barycenter optimization in optimal transport.

New algorithm solves unbalanced optimal transport on trees in quasi-linear time.

The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of the transport paths is studied. These results generalize parts of Bertrand & Puel…

Paper tackles distribution matching by partially matching distributions, achieving robust results.

New optimal transport divergences derived from scoring functions.

We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we apply the latter to prove suitable generalizations of Brenier's theorem of existence of optimal ma…

Generative sampler learns velocity fields for efficient posterior inference.

A scalable algorithm approximates Wasserstein Barycenters using neural networks.

In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we prove that th…

Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is however piece-wise constant (the sorting permutation of a vector does not change if th…