arXiv Machine Learning July 28, 2026 By Ao Xu, Tieru Wu

Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning

Read the original on arXiv Machine 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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Statistics ML

Sep 4

Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing

The paper presents a new duality formulation for the Gromov‑Wasserstein distance that applies to all finitely supported metric‑measure spaces, with and without entropic regularization. Using this duality, the authors derive sample‑complexity bounds and limit distributions for empirical GW distances, and introduce algorithms with formal convergence guarantees. These results enable a principled, efficient method for testing isomorphism between distributions on graphs with a fixed number of nodes based on samples.

By Gabriel Rioux, Joanna Marks, Riccardo Passeggeri, Ziv Goldfeld

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.

By Edivaldo Lopes dos Santos, Leandro Vicente Mauri, Washington Mio, Tom Needham

arXiv Machine Learning

Sep 15

Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications

arXiv:2608.27500v3 Announce Type: replace-cross Abstract: Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport...

By James Hyun, Fran\c{c}ois G. Meyer

arXiv Machine Learning

Jul 28

On a linear fused Gromov-Wasserstein distance for graph structured data

arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.

By Dai Hai Nguyen, Koji Tsuda

rag

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.

By Junhyoung Chung, Euijong Song, Won Hwa Kim, Gunwoong Park

benchmarks

arXiv Machine Learning

Aug 6

Multimodal Alignment Through Joint Kernel Entropic Gromov--Wasserstein Optimal Transport

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.

By Yixuan Florence Wu, Yilun Zhu, Naichen Shi

rag diffusion multimodal safety

One email a morning, machine-written

Related stories

Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing

The Observable Wasserstein Distance

Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications

On a linear fused Gromov-Wasserstein distance for graph structured data

Convex Distance Operator Transport: A Convex and Geometry-Preserving Formulation

Multimodal Alignment Through Joint Kernel Entropic Gromov--Wasserstein Optimal Transport