arXiv Machine Learning June 9, 2026 By Ofek Amran, Tom Gilat, Ron Levie

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation

Read the original on arXiv Machine Learning →

arXiv:2602. 08785v2 Announce Type: replace Abstract: Generalization and approximation capabilities of message passing graph neural networks (MPNNs) are often studied by defining a compact metric on a space of input graphs under which MPNNs are equicontinuous.

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arXiv Machine Learning

Sep 2

Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials

arXiv:2609.00528v1 Announce Type: new Abstract: We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy su...

By Pingbing Ming, Han Wang

arXiv Machine Learning

Jun 30

Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks

arXiv:2603. 14846v3 Announce Type: replace Abstract: We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices).

By Eran Rosenbluth

arXiv AI

Aug 25

Which Algorithms Can Graph Neural Networks Learn?

arXiv:2602.13106v2 Announce Type: replace-cross Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...

By Solveig Wittig, Antonis Vasileiou, Robert R. Nerem, Timo Stoll, Floris Geerts, Yusu Wang, Christopher Morris

efficiency

arXiv Machine Learning

Sep 1

Graph Representational Learning: When Does More Expressivity Hurt Generalization?

arXiv:2505.11298v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive per...

By Sohir Maskey, Raffaele Paolino, Fabian Jogl, Gitta Kutyniok, Johannes F. Lutzeyer

Hugging Face Trending Papers

Jul 29

Universality and Approximation Rates of Graph Neural Networks with Random Features

We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically.

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

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Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials

Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks

Which Algorithms Can Graph Neural Networks Learn?

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