arXiv:2608. 16506v1 Announce Type: cross Abstract: Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets.
arXiv:2407. 01718v2 Announce Type: replace-cross Abstract: Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis.
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
arXiv:2607. 16178v1 Announce Type: cross Abstract: In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure.
arXiv:2608. 04234v1 Announce Type: cross Abstract: We study the problem of aligning data from multiple modalities into a shared representation space, focusing on settings where strong pretrained unimodal encoders are available but cross-modal paired data are scarce.
arXiv:2606. 14023v1 Announce Type: cross Abstract: Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions.
arXiv:2605. 00337v2 Announce Type: replace Abstract: Sampling the distribution of collective variables (CVs) and estimating the associated free energy surface are crucial problems in statistical physics, as they underpin a better understanding of chemical reactions and conformational transitions.
arXiv:2511. 17812v3 Announce Type: replace-cross Abstract: Flow matching models effectively represent complex distributions, yet estimating expectations of functions of their outputs remains challenging under limited sampling budgets.
The growing number of medical vision foundation models highlights the need for effective model selection. However, mainstream selection methods rely on exhaustive fine-tuning, which is computationally expensive.
arXiv:2606. 24987v1 Announce Type: cross Abstract: Optimal transport (OT) has become a central language for comparing probability measures, but exact balanced OT is often both too rigid for data with missing, created, or destroyed mass and subject to unfavorable high-dimensional sample complexity.
Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored.
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. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.