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: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
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
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 $\sphere^{n-1}\subset\R^n$.
By Gopal Anantharaman
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
The paper reviews the use of optimal transport for comparing undirected, unweighted graphs, focusing on three main distances: Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein. It discusses closed-form solutions for the Wasserstein distance in one dimension, how transport plans identify influential nodes after perturbations, and derives spectral bounds for the Bures-Wasserstein distance to avoid full decompositions. The authors evaluate these distances on synthetic clustering data and a real-world time‑series network for anomaly detection.
By James Hyun, Fran\c{c}ois G. Meyer
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
The paper investigates whether placing class prototypes on a hyperbolic manifold (Poincaré ball) rather than a Euclidean space improves the satisfaction of a tree‑structured regularizer in hierarchical classification. Experiments on WikiArt show that hyperbolic prototypes better preserve nearest‑neighbor topology (higher sibling and cousin recall) across multiple tree definitions, while Euclidean prototypes perform similarly to logistic regression on raw features and only hyperbolic models improve local retrieval. The study provides empirical evidence that the choice of latent geometry can affect the fidelity of tree‑structured regularization in real data.
By Peter Flo, Luca Grossmann
arXiv:2606. 18520v1 Announce Type: cross Abstract: Computing geometric representations of data is a cornerstone of modern machine learning, typically achieved by training dual encoders which map queries and documents into a shared embedding space.
By Prashant Gokhale, Piotr Indyk, Yuhao Liu, Sandeep Silwal, Tony Chang Wang, Haike Xu
arXiv:2609.36302v1 Announce Type: new
Abstract: While foundation models have revolutionized natural language processing and computer vision by leveraging universal vocabularies, Graph Machine Learnin...
By Ben Finkelshtein, Andr\'{e} Linhares, Petar Veli\v{c}kovi\'{c}, Bryan Perozzi, Mikhail Galkin
We study a tree-structured regularizer over class-prototype layouts in a hierarchical-classification model and ask whether the choice of latent manifold for the prototypes (Euclidean R^d vs. the Poinc...
The paper introduces the Support Vector Graph (SVG), a graph index for vector search that uses kernel methods to guarantee navigability in both metric and non‑metric vector spaces, such as inner product similarity. It shows that popular indices like HNSW and DiskANN are special cases of SVG, and proposes SVG‑L0, which adds an ℓ₀ sparsity constraint to enforce bounded out‑degree while maintaining computational efficiency.
By Mariano Tepper, Ted Willke