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 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 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 Machine Learning
1d ago
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.
arXiv Machine Learning
2d ago
High-dimensional nonparametric changepoint detection via low-rank degree-two density projection
arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.
arXiv Machine Learning
Jun 2
Convex Distance Operator Transport: A Convex and Geometry-Preserving Formulation
arXiv:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.
arXiv AI
Jun 9
A Topological Characterization of Graph Neural Networks via Stochastic Block Model Embeddings on the n-Sphere
arXiv:2606. 07598v1 Announce Type: cross Abstract: We propose a topological framework for comparing trained Graph Neural Networks (GNNs) by mapping the Stochastic Block Models (SBMs) induced on the graphon-signal space of a Message Passing Neural Network (MPNN) onto the unit $n$-sphere $\sphere^{n-1}\subset\R^n$.
arXiv Machine Learning
Jun 16
Online Realizable Regression and Applications for ReLU Networks
arXiv:2602. 19172v2 Announce Type: replace Abstract: Realizable online regression can behave very differently from online classification.
arXiv Machine Learning
5d ago
Gradient-Free Warm-Start Library Recovery: an Amortized-Regret Separation
arXiv:2606. 21253v2 Announce Type: replace Abstract: Continual learning that is gradient-free, local, online, and append-only is attractive for edge and streaming deployment, but its value is usually argued informally.