The example shows the learned IT map with high w =2 0 approximating the ET map.

In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image.

Neural Information Processing Systems http://nips.cc/

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose \texttt{FairSinkhorn}, a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalised OT problem, for which we derive novel finite-sample complexity guarantees. This result is of independent interest as it can be generalized to arbitrary convex penalties. Our second strategy leverages bilevel optimization to learn a ground cost that induces a fair OT solution, and we establish a bound guaranteeing that the learned cost yields fair matchings on unseen data. Finally, we present empirical results that illustrate the trade-offs between fairness and performance.

Topological data analysis (TDA) has been used successfully in a wide array of applications, for instance in medical (Nicolau et al., 2011) or material (Hiraoka et al., 2016) sciences, computer vision (Li et al., 2014) or to classify NBA players (Lum et al., 2013).

Optimal transport (OT) has emerged as a fundamental computational tool across many areas, including machine learning, computer vision, statistics, and biology [Arjovsky et al., 2017, Peyr e and Cuturi, 2019, Schiebinger et al., 2019, Bonneel and Digne, 2023]. It provides a principled framework for comparing probability distributions, and it has a rich mathematical history [Villani et al., 2008]. While the combination of practical utility and deep mathematical theory has led to the broad adoption of OT ideas in mathematics, science, and engineering, finding ways to scale OT solutions and make them interpretable remains a fundamental research question [Cuturi et al., 2023, Khamis et al., 2024]. In particular, OT typically suffers from the curse of dimensionality [Chewi et al., 2025], and regularized estimators may lack sparsity [Genevay et al., 2019]. A long line of work has focused on making OT scalable and interpretable through regularization. The most classical of these is entropic regularization, which yields a strictly convex program that can be solved via Sinkhorn scaling [Sinkhorn, 1967, Cuturi, 2013]. More recent work has sought to increase efficiency and interpretability through quadratic regularization [Blondel et al., 2018, Lorenz et al., 2021], as well as low-rank factorizations [Forrow et al., 2019, Scetbon et al., 2021]. These methods show promise in biological applications, particularly in single-cell RNA sequencing analysis [Klein et al., 2025]. Another closely related set of recent works attempts to include sparsity in the OT map using elastic costs Cuturi et al. [2023], Klein et al. [2024], Chen et al. [2025].

The example shows the learned IT map with high w =2 0 approximating the ET map.

In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image.

Neural Information Processing Systems http://nips.cc/

Partial domain adaptation (PDA) problem requires aligning cross-domain samples while distinguishing the outlier classes for accurate knowledge transfer. The widely used weighting framework tries to address the outlier classes by introducing the reweighed source domain with a similar label distribution to the target domain. However, the empirical modeling of weights can only characterize the sample-wise relations, which leads to insufficient exploration of cluster structures, and the weights could be sensitive to the inaccurate prediction and cause confusion on the outlier classes. To tackle these issues, we propose a Bi-level Unbalanced Optimal Transport (BUOT) model to simultaneously characterize the sample-wise and class-wise relations in a unified transport framework. Specifically, a cooperation mechanism between sample-level and class-level transport is introduced, where the sample-level transport provides essential structure information for the class-level knowledge transfer, while the class-level transport supplies discriminative information for the outlier identification. The bi-level transport plan provides guidance for the alignment process. By incorporating the label-aware transport cost, the local transport structure is ensured and a fast computation formulation is derived to improve the efficiency. Introduction Traditional machine learning usually follows the assumption that training data and test data come from the same distribution. Corresponding author Email address: rchuanx@mail.sysu.edu.cn This distribution discrepancy can degrade the performance of machine learning models when they are deployed in new environments or domains. To overcome this challenge, unsupervised domain adaptation (UDA) [1, 2] has been developed to transfer knowledge from the labeled source domain to the unlabeled target domain, enabling the models trained on the source domain that can generalize well to the target domain. Usually, UDA methods train the model using source domain samples to minimize the source domain classification error and then use appropriate methods to eliminate the cross-domain divergence.