相关论文: Scalable Unbalanced Sobolev Transport for Measures…

Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…

Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…

Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…

Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…

In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that…

We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and related conservative systems as concave maximization…

We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…

In this paper, we explore the idea of combining GCNs into one model. To that end, we align the weights of different models layer-wise using optimal transport (OT). We present and evaluate three types of transportation costs and show that…

Evaluating lesion evolution in longitudinal CT scans of can cer patients is essential for assessing treatment response, yet establishing reliable lesion correspondence across time remains challenging. Standard bipartite matchers, which rely…

Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads to enhanced numerical complexity and a denser transport plan. Many formulations impose a global constraint on the transport plan, for instance…

We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit…

Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…

We introduce optimal transport (OT) as a physics-based intermediate event representation for weakly supervised anomaly detection. With only $0.5\%$ injection of resonant signals in the LHC Olympics benchmark datasets, the OT-augmented…

This paper reviews recent advancements in the application of optimal transport (OT) to multivariate distribution-free nonparametric testing. Inspired by classical rank-based methods, such as Wilcoxon's rank-sum and signed-rank tests, we…

This paper introduces a framework that utilizes the Safe Screening technique to accelerate the optimization process of the Unbalanced Optimal Transport (UOT) problem by proactively identifying and eliminating zero elements in the sparse…

While the continuous Entropic Optimal Transport (EOT) field has been actively developing in recent years, it became evident that the classic EOT problem is prone to different issues like the sensitivity to outliers and imbalance of classes…

Out-of-distribution (OOD) data poses serious challenges in deployed machine learning models, so methods of predicting a model's performance on OOD data without labels are important for machine learning safety. While a number of methods have…

Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention…

Modern autonomous vehicles and robots utilize versatile sensors for localization and mapping. The fidelity of these maps is paramount, as an accurate environmental representation is a prerequisite for stable and precise localization. Factor…

The inherent safety alignment of Large Language Models (LLMs) is prone to erosion during fine-tuning, even when using seemingly innocuous datasets. While existing defenses attempt to mitigate this via data selection, they typically rely on…