arXiv AI June 9, 2026 By Gopal Anantharaman

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 $\sphere^{n-1}\subset\R^n$.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.

arXiv Machine Learning

Jul 14

Distance-Preserving Embeddings in Inhomogeneous Random Graphs

arXiv:2607. 10074v1 Announce Type: new Abstract: Graph machine learning provides powerful tools for understanding complex networks and learning meaningful node representations.

By My Le, Luana Ruiz, Souvik Dhara

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arXiv Machine Learning

Jul 30

On the Rademacher Complexity of Graph Neural Networks: Unifying Expressivity and Geometry

arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.

By Martin Carrasco, Caio F. Deberaldini Netto, Vahan A. Martirosyan, Ehimare Okoyomon, Caterina Graziani

arXiv Machine Learning

Jun 10

$k$-Nearest Neighbors in Gromov--Wasserstein Space

arXiv:2606. 10295v1 Announce Type: cross Abstract: The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry.

By Kaitlyn Hohmeier, Nicolas Fraiman, Caroline Moosmueller

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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}.

By Matteo Pegoraro

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arXiv Machine Learning

Jun 16

Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs

arXiv:2602. 10031v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing.

By Antonis Vasileiou, Juan Cervino, Pascal Frossard, Charilaos I. Kanatsoulis, Christopher Morris, Michael T. Schaub, Pierre Vandergheynst, Zhiyang Wang, Guy Wolf, Ron Levie

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.

By Ao Xu, Tieru Wu

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Related stories

Distance-Preserving Embeddings in Inhomogeneous Random Graphs

On the Rademacher Complexity of Graph Neural Networks: Unifying Expressivity and Geometry

$k$-Nearest Neighbors in Gromov--Wasserstein Space

Persistence Spheres: a Bi-continuous Linear Representation of Measures for Partial Optimal Transport

Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs

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