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.
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.
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arXiv Machine Learning
Jul 30
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}.
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
4d ago
Averaged Mirror Descent and Dual Gradient Methods: Convergent Algorithms for Entropic Gromov-Wasserstein Problems
The paper studies algorithms for computing the Entropic Gromov-Wasserstein (EGW) distance, a measure of discrepancy between metric measure spaces. It introduces Averaged Mirror Descent (AMD), which averages successive Mirror Descent steps and is proven to converge for any cost function, and shows that a dual gradient method with a fixed step size also converges for arbitrary costs, even when iterations are inexact. Empirical comparisons demonstrate that both AMD and the dual gradient method succeed on cases where classical Mirror Descent fails.
arXiv Machine Learning
Jun 9
Global Convergence of Wasserstein Policy Gradient for Entropy-Regularized Reinforcement Learning
arXiv:2605. 26078v3 Announce Type: replace Abstract: Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions.
arXiv Machine Learning
Jun 9
Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation
arXiv:2606. 07931v1 Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes.
arXiv Machine Learning
Sep 24
Task-Induced Riemannian Metrics for Vision Transformer Feature Spaces
arXiv:2609.27988v1 Announce Type: cross Abstract: Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direc...
arXiv Machine Learning
Jul 28
Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
arXiv Machine Learning
Jun 2
Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetry
arXiv:2511. 01064v3 Announce Type: replace-cross Abstract: Variational inference (VI) approximates a target density $p$ by the best match $q$ in a family of tractable distributions.
arXiv AI
Aug 24
GRALIS: Fusing Coalition and Gradient Attribution with Closed-Form Conservation Error and Finite-Sample Guarantees
GRALIS (Gradient‑Riesz Averaged Locally‑Integrated Shapley) merges coalition‑based and gradient‑based post‑hoc XAI techniques into a single estimator. It provides two certified guarantees: an exact closed‑form completeness deficit and a finite‑sample bound on the self‑normalized ratio. The method is grounded in a representation‑theoretic result that uniquely characterizes additive, linear, continuous attribution functionals, and it is experimentally illustrated on breast histology imaging.
arXiv Machine Learning
Aug 4
Computational and Statistical Guarantees of the \textit{c}-Rectified flow
arXiv:2608. 02487v1 Announce Type: cross Abstract: Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.
arXiv Machine Learning
Sep 15
CyclOT: Learning Quadratic Optimal Transport Maps via Synchronized Forward-Backward Interpolants
arXiv:2609.13892v1 Announce Type: cross Abstract: We study the recovery of forward and reverse quadratic optimal-transport maps from unpaired samples in high dimensions. We introduce a bidirectional...