SPG learns policies on permutation matrices using Sinkhorn layers.
problem Optimizing permutations for tasks like sorting, ranking, and matching.
method Introduces Sinkhorn Policy Gradient (SPG) algorithm with a temperature-controlled Sinkhorn layer.
result SPG agents perform competitively and are more data-efficient than baseline methods on matching tasks.
The Sinkhorn flow converges to a Wasserstein mirror gradient flow from the Sinkhorn algorithm.
problem Optimizing joint distributions using the Sinkhorn algorithm.
method Wasserstein mirror gradient flow derived from the Sinkhorn algorithm.
result The Sinkhorn flow converges to a Wasserstein mirror gradient flow.
Paper solves barycenter of probability distributions using Sinkhorn divergence.
problem Computing the barycenter of a set of probability distributions under the Sinkhorn divergence.
method Recast as unconstrained functional optimization and develop Sinkhorn Descent (SD) method.
result SD converges to a stationary point at a sublinear rate and asymptotically finds a global minimizer.
New framework optimizes decisions under uncertainty considering causal and continuous data.
problem Optimizing decisions under uncertain distributions with causal and continuous data structures.
method Developed a framework using Causal Sinkhorn DRO with Soft Regression Forest decision rules.
result Framework provides interpretable and tractable decision rules for optimizing under uncertainty.
A new algorithm for training generative models using Sinkhorn divergence.
problem Training generative adversarial networks (GANs).
method Sinkhorn Natural Gradient (SiNG) algorithm for steepest descent on probability space.
result Explicit expression and efficient evaluation of the Sinkhorn information matrix (SIM).
New insights into Sinkhorn approximation's smoothness and differentiation.
problem Lack of accurate and differentiable approximation of Wasserstein distance.
method Characterized differential properties of Sinkhorn distance and provided an efficient gradient algorithm.
result The original Sinkhorn distance is as smooth as its regularized version, enabling better learning and optimization.
The Sinkhorn flow is a gradient flow in a nonlocal Wasserstein geometry.
problem Entropy-regularized optimal transport and its applications.
method Thermodynamic interpretation of the Sinkhorn algorithm.
result The Sinkhorn flow is the gradient flow of entropy in a nonlocal Wasserstein geometry.
The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.
New algorithm estimates barycenters of distributions using Frank-Wolfe.
problem Estimating the average of arbitrary probability distributions.
method Frank-Wolfe optimization for Sinkhorn divergence, incrementally populating support.
result Converges in both discrete and continuous distributions, with proven rates.
New perspective on Sinkhorn algorithm using stochastic mirror descent.
problem Optimal transport with unbounded domain and non-smooth objective.
method Stochastic mirror descent applied to relative smoothness.
result Sinkhorn algorithm as a special case of stochastic mirror descent.
Paper analyzes convergence of Sinkhorn algorithm for discrete probability measures on torus.
problem Achieving exponential convergence of Sinkhorn algorithm in general settings.
method Coupling by reflection techniques for controlled diffusions on the torus.
result Proves pointwise exponential convergence of Sinkhorn iterates and their gradient.
This paper tackles Sinkhorn DRO by reformulating it as a bilevel program and proposes sampling-based algorithms.
problem Distributionally robust optimization with ambiguity sets defined via the Sinkhorn discrepancy.
method Primal perspective reformulation as a bilevel program, double-loop and single-loop sampling-based algorithms.
result Simultaneously obtain the optimal robust decision and the worst-case distribution.
A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.
problem Efficiently retrieving patterns from large datasets of weighted point clouds.
method Derived retrieval dynamics as a SHK gradient flow, discretized for a deterministic algorithm.
result Proved basin invariance, geometric convergence, and robust recovery from perturbations.
New algorithm solves Schrödinger bridge problem with mismatched channels.
problem Solving Schrödinger bridge problem with input and noise channel mismatch.
method Design of a Sinkhorn recursion with memory for nonlinear PDEs.
result Demonstrates solving control-affine Schrödinger bridge problem.
New methods improve stability of Sinkhorn algorithm in machine learning.
problem Stability of Sinkhorn semigroups in high-dimensional settings.
method Semigroup analysis based on contraction coefficients and Lyapunov-type operator-theoretic techniques.
result Unified and simplified arguments in Sinkhorn algorithm stability.
It is of increasing importance to develop learning methods for ranking. In contrast to many learning objectives, however, the ranking problem presents difficulties due to the fact that the space of permutations is not smooth. In this paper, we examine the class of rank-linear objective functions, which includes popular…
Paper tackles robust model training with a new stochastic algorithm.
problem Training robust models against data distribution shift.
method Derives a novel dual formulation and proposes a nested stochastic gradient descent algorithm.
result Establishes polynomial iteration and sample complexities for large-scale DRO problems.
A new gradient flow framework for distributionally robust optimization.
problem Optimizing under uncertainty with worst-case distributional constraints.
method Gradient flow theory applied to distributionally robust optimization.
result Practical algorithms for sampling from worst-case distributions.
Improved algorithms for optimal transport with better complexity bounds.
problem Efficiency of algorithms for solving optimal transport problems.
method Greenkhorn, APDAMD, and accelerated Sinkhorn algorithms with improved complexity bounds.
result Improved complexity bounds for Greenkhorn, APDAMD, and accelerated Sinkhorn algorithms.
Improved online Sinkhorn algorithm for large-scale data processing.
problem Efficiency of Sinkhorn algorithm for large-scale data streams.
method Revisit and improve convergence analysis of online Sinkhorn algorithm, introduce compressed online Sinkhorn algorithm.
result New faster convergence rate for online Sinkhorn algorithm under certain conditions.
New discretization scheme for Wasserstein gradient flows using Schrödinger bridges.
problem Computing Wasserstein gradient flows efficiently and without score functions.
method Iterated Schrödinger bridge approximation with particle-based Sinkhorn algorithm.
result The scheme converges to Wasserstein gradient flows for certain flows, including heat flow.
Continuous-time Sinkhorn flow generalizes and unifies existing dynamics.
problem Entropy-regularized optimal transport problems.
method Continuous-time mirror descent framework.
result Unified perspective on various dynamics in ML and math.
The Sinkhorn-Knopp derivatives converge with linear rate.
problem Optimal transport problem with entropic regularization.
method Iterative proportional fitting procedure.
result Derivatives converge with linear rate.
New method speeds up computation of Sinkhorn distances for large datasets.
problem Quadratic time and memory requirements of standard Sinkhorn distance computation.
method Combining Nyström method and Sinkhorn scaling for faster approximations.
result Accurate approximations of Sinkhorn distances on massive datasets.
SAE learns generative models via optimal transport.
problem Learning generative models with optimal transport.
method Minimizes p-Wasserstein distance via Sinkhorn algorithm.
result SAE works with various metric spaces and priors.
A new algorithm screens negligible components to efficiently approximate optimal transport distances.
problem Efficiently approximating the Sinkhorn distance between discrete measures.
method Screening of negligible components in the dual solution of the regularized Sinkhorn problem.
result Screenkhorn algorithm provides provable guarantees with smaller computational complexity.
Improved Sinkhorn algorithm for UOT with near-linear complexity.
problem Solving the entropic regularized Unbalanced Optimal Transport problem efficiently.
method Geometric convergence analysis of Sinkhorn updates and primal solution properties.
result Near-linear time complexity for finding ε-approximate UOT solutions. Analyzed a generative model framework through Wasserstein Gradient Flow.
problem Generative modeling challenges.
method Wasserstein Gradient Flow (WGF) interpretation of Drifting Models (GMD).
result Different algorithms correspond to specific limiting points of WGFs on various divergences.
A new algorithm for learning shallow neural networks with infinite width.
problem Learning shallow over-parameterized neural networks.
method Sinkhorn proximal algorithm approximating mean field learning dynamics.
result The algorithm performs gradient descent of the free energy associated with the risk functional.
Survey of Sinkhorn algorithm for optimal transport, emphasizing its geometric origins.
problem Solving optimal transport problems efficiently and accurately.
method Discretization of a non-linear integral equation.
result Geometric interpretation and discretization of the Sinkhorn algorithm.
SNS accelerates Sinkhorn algorithm with sparse Newton iterations.
problem Slow runtime of Sinkhorn algorithm for optimal transport.
method Early stopping and Newton-type subroutine for matrix scaling steps.
result SNS converges orders of magnitude faster than Sinkhorn.
This paper introduces Gumbel-Sinkhorn networks for learning latent matchings.
problem Learning in latent variable models with permutations is difficult due to combinatorial intractability.
method Approximates maximum-weight matching using the Sinkhorn operator, extending Gumbel-Softmax.
result Demonstrates effectiveness on sorting, jigsaw puzzles, and neural signal identification tasks.
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
This work studies the statistical performance of Sinkhorn iterations in estimating Schrödinger bridges.
problem Estimating Schrödinger bridges with limited samples.
method Intermediate Sinkhorn iterations applied to the time-dependent drifts of SDEs.
result Established a statistical bound on the squared total variation error of Sinkhorn bridge iterations.
Paper uses Sinkhorn distances to improve imitation learning effectiveness.
problem Improving imitation learning algorithms by comparing occupancy measures.
method Formulates imitation learning as Sinkhorn distance minimization, combining optimal transport and cosine distances.
result Proposes a new critic network and transport plan that guide imitation learning.
Optimizes distributions robustly with Sinkhorn distance.
problem Distributionally robust optimization with Wasserstein distance.
method Convex programming dual reformulation, stochastic mirror descent algorithm.
result Demonstrates superior performance in synthetic and real data.
cuRegOT accelerates GPU-based entropic OT solving.
problem Slow convergence and high computational cost of optimal transport on GPUs.
method High-performance GPU solver with algorithmic and architectural optimizations.
result Significant speedups over state-of-the-art solvers.
This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.
problem Finite-dimensional solutions for general Gaussian multivariate models.
method Recursive formulation of the Sinkhorn algorithm for Gaussian models, including closed form expressions of entropic transport maps and Schrödinger bridges.
result Refined convergence analysis of Gaussian Sinkhorn algorithms.
This paper generalizes Sinkhorn algorithm for unbalanced optimal transport.
problem Handling distributions with different total mass and robustness to outliers.
method Alternates between standard Sinkhorn updates and pointwise application of a contractive function.
result Defines Sinkhorn divergences that are differentiable, positive, definite, convex, and robust.
OTSeg uses multi-prompt Sinkhorn attention to improve zero-shot semantic segmentation.
problem Leveraging pre-trained CLIP knowledge to align text embeddings with pixel embeddings.
method OTSeg employs Multi-Prompts Sinkhorn (MPS) and Multi-Prompts Sinkhorn Attention (MPSA) to enhance semantic feature matching.
result OTSeg achieves state-of-the-art performance in zero-shot semantic segmentation tasks.
Develops a new algorithm to calibrate signed datasets to specified marginals.
problem Calibrating signed datasets to specified marginals.
method Extends Schrödinger-Fortet-Sinkhorn paradigm to sign-indefinite multi-dimensional arrays.
result Proposes an optimization problem to update a sign-indefinite prior to match given marginals.
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in …
Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.
problem Convergence and approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
method Analysis of convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
result Strictly weaker convergence in 2-Sinkhorn divergence for Gaussian measures compared to exact 2-Wasserstein distance.
New method builds volatility surfaces from quotes without arbitrage.
problem Building arbitrage-free implied volatility surfaces from market data.
method Sinkhorn's algorithm for optimal transport, proven convergence.
result Efficient numerical procedure for volatility surface construction.
W-Flow generates images in one step, faster and better than multi-step methods.
problem Efficiently generating images from a simple reference distribution to a target data distribution.
method W-Flow uses Wasserstein gradient flows to transform the reference distribution to the target distribution in a single step, trained with Sinkhorn divergence.
result W-Flow achieves state-of-the-art results in ImageNet 256imes256 generation with improved mode coverage and faster sampling. Paper proposes a robust hypothesis testing method using Sinkhorn distance.
problem Hypothesis testing for small samples.
method Data-driven approach using Sinkhorn uncertainty sets.
result The method provides a more flexible detector compared to Wasserstein robust test.
Paper proposes SinkhornDRL for distributional RL using Sinkhorn divergence and regularized Wasserstein loss.
problem Improving distributional reinforcement learning by minimizing Bellman return distribution differences.
method Introduces SinkhornDRL, a distributional RL algorithm using Sinkhorn divergence and regularized Wasserstein loss.
result SinkhornDRL consistently outperforms or matches existing algorithms on Atari games, especially in multi-dimensional reward settings.
Optimal transport with f-divergence regularization using generalized Sinkhorn algorithm.
problem Optimal transport with f-divergence regularization. method Generalized Sinkhorn algorithm for solving optimal transport problems with various f-divergences. result Strong duality holds, optimums are attained, and convergence to an optimal solution is guaranteed under certain conditions.