The paper introduces BROT, a two‑step approach for estimating optimal transport maps. First, it computes the unregularized OT plan, then fits a deep neural network to the resulting barycentric targets using least‑squares regression. The authors prove that, under standard regularity conditions, BROT achieves the minimax convergence rate when the true OT map is Lipschitz, and demonstrate its effectiveness on synthetic data, images, and downstream tasks such as single‑cell perturbation prediction and unsupervised domain adaptation.
By Kunwoong Kim, Insung Kong, Yongdai Kim
The paper introduces Distribution‑Conditioned Transport (DCT), a framework that learns transport maps conditioned on embeddings of source and target distributions, allowing generalization to unseen distribution pairs. DCT supports semi‑supervised learning for distributional forecasting by leveraging distributions observed at only one condition. It is agnostic to the transport mechanism and is demonstrated on synthetic benchmarks and four biological applications, including batch effect transfer in single‑cell genomics and modeling T‑cell receptor sequence evolution.
By Nic Fishman, Gokul Gowri, Paolo L. B. Fischer, Marinka Zitnik, Omar Abudayyeh, Jonathan Gootenberg
arXiv:2602. 01179v2 Announce Type: replace Abstract: Gradual domain adaptation (GDA) aims to mitigate domain shift by progressively adapting models from the source domain to the target domain via intermediate domains.
By Zhichao Chen, Zhan Zhuang, Yunfei Teng, Hao Wang, Fangyikang Wang, Zhengnan Li, Tianqiao Liu, Haoxuan Li, Zhouchen Lin
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
By Sivaraman Balakrishnan
arXiv:2412. 18081v3 Announce Type: replace-cross Abstract: We study Heterogeneous Transfer Learning (HTL) for high-dimensional regression with differing feature sets.
By Jae Ho Chang, Massimiliano Russo, Subhadeep Paul
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
By Fanghui Song, Zhongjian Wang, Jiebao Sun
arXiv:2510. 04602v4 Announce Type: replace-cross Abstract: Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space.
By Eduardo Fernandes Montesuma, Yassir Bendou, Mike Gartrell
arXiv:2606. 25347v1 Announce Type: new Abstract: Exemplar-free class-incremental learning (EFCIL) requires stable decision boundaries within a shifting feature space.
By Hongye Xu, Bartosz Krawczyk
arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.
By Gabriel Peyr\'e
arXiv:2509. 09371v2 Announce Type: replace-cross Abstract: Distributionally robust optimization (DRO) protects statistical learning against distributional shifts by optimizing the worst-case performance over a set of perturbed distributions.
By Zitao Wang, Nian Si, Molei Liu
arXiv:2602.19600v2 Announce Type: replace
Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
By Xinyu Tian, Xiaotong Shen