arXiv Machine Learning
Jun 4
Cone-Compatible Monge Geometry for High-Dimensional Ordered Optimal Transport
arXiv:2606. 04695v1 Announce Type: new Abstract: High-dimensional optimal transport is seldom available in closed form.
Persistence Spheres: a Bi-continuous Linear Representation of Measures for Partial Optimal Transport
arXiv:2603. 15384v2 Announce Type: replace-cross Abstract: We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}.
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arXiv Machine Learning
Jun 25
The Urysohn Ladder: Recursive Metric Contraction for Scalable Continual Learning
arXiv:2512. 18471v2 Announce Type: replace Abstract: Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference.
arXiv Machine Learning
Jun 25
Structured Approximations of Measures
arXiv:2310. 09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints.
arXiv Statistics ML
Aug 27
Barycentric Weak Inner-Product Gromov-Wasserstein
The paper introduces a weak Gromov-Wasserstein (wGW) framework that compares source relations with relations between target conditional laws, focusing on inner-product relations and preserving conditional means. It defines the barycentric weak inner-product GW (wIGW) distance, proves existence of minimizers under finite second moments, and presents a ridge-regularized dual formulation leading to an iterative algorithm for finitely supported measures. Experiments on point clouds, graphs, and a PBMC multiome study demonstrate that mean-preserving target refinements can incur zero cost and improve atlas-based cell type transfer.
arXiv AI
Jun 16
Optimal Transport for Machine Learners
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.
arXiv Statistics ML
Sep 17
Approximating Measures on Function Spaces: Transport and Truncation
arXiv:2609.17802v1 Announce Type: cross Abstract: Measures on function spaces arise throughout Bayesian inverse problems and generative modeling, often with low-dimensional structure relative to a tr...
Hugging Face Trending Papers
Sep 1
Sierpiński--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation
This paper introduces the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. The SK-Wasserstein distance, denoted $d_{\mathrm{SK}}$, maps diagram points and their...
arXiv Machine Learning
Jun 30
Learning from samples: inverse problems over measures
arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.
arXiv AI
Jun 8
A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.
arXiv Statistics ML
Aug 25
Q-Learning with Stable Infinite-Dimensional Linear Function Approximation
arXiv:2608.22636v1 Announce Type: cross Abstract: Q-learning with linear function approximation can be unstable because an arbitrary approximation architecture need not preserve the Bellman contracti...
arXiv Machine Learning
Aug 31
SinkSLOT: Sinkhorn via Sparse Lifted Optimal Transport
arXiv:2608. 28262v1 Announce Type: new Abstract: Entropic optimal transport (EOT) has been shown to offer a computationally tractable approximation to exact optimal transport.
arXiv Machine Learning
Aug 18
The Observable Wasserstein Distance
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.