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Graph neural networks are designed to learn functions on graphs. Typically, the relevant target functions are invariant with respect to actions by permutations. Therefore the design of some graph neural network architectures has been…

Machine Learning · Statistics 2022-11-03 Ningyuan Huang , Soledad Villar

Incorporating spectral information to enhance Graph Neural Networks (GNNs) has shown promising results but raises a fundamental challenge due to the inherent ambiguity of eigenvectors. Various architectures have been proposed to address…

Machine Learning · Computer Science 2024-06-07 Bohang Zhang , Lingxiao Zhao , Haggai Maron

The ability of graph neural networks (GNNs) to count homomorphisms has recently been proposed as a practical and fine-grained measure of their expressive power. Although several existing works have investigated the homomorphism counting…

Machine Learning · Computer Science 2024-10-07 Junru Zhou , Muhan Zhang

Research on the theoretical expressiveness of Graph Neural Networks (GNNs) has developed rapidly, and many methods have been proposed to enhance the expressiveness. However, most methods do not have a uniform expressiveness measure except…

Machine Learning · Computer Science 2024-06-04 Yanbo Wang , Muhan Zhang

Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the $k$-dimensional Weisfeiler-Leman ($k$WL) test, a widely-recognized method for verifying…

Machine Learning · Computer Science 2024-03-29 Matthias Lanzinger , Pablo Barceló

We study and compare different Graph Neural Network extensions that increase the expressive power of GNNs beyond the Weisfeiler-Leman test. We focus on (i) GNNs based on higher order WL methods, (ii) GNNs that preprocess small substructures…

Machine Learning · Computer Science 2022-02-01 Pál András Papp , Roger Wattenhofer

The message-passing scheme is the core of graph representation learning. While most existing message-passing graph neural networks (MPNNs) are permutation-invariant in graph-level representation learning and permutation-equivariant in node-…

Machine Learning · Computer Science 2022-11-22 Chang Liu , Yuwen Yang , Yue Ding , Hongtao Lu

Graph Neural Networks (GNNs) have emerged as prominent models for representation learning on graph structured data. GNNs follow an approach of message passing analogous to 1-dimensional Weisfeiler Lehman (1-WL) test for graph isomorphism…

Machine Learning · Computer Science 2022-03-18 Mohammed Haroon Dupty , Wee Sun Lee

Graph neural networks (GNNs) are the standard for learning on graphs, yet they have limited expressive power, often expressed in terms of the Weisfeiler-Leman (WL) hierarchy or within the framework of first-order logic. In this context,…

Machine Learning · Computer Science 2026-04-22 Amirreza Akbari , Amauri H. Souza , Vikas Garg

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive…

Machine Learning · Computer Science 2021-06-15 Cristian Bodnar , Fabrizio Frasca , Yu Guang Wang , Nina Otter , Guido Montúfar , Pietro Liò , Michael Bronstein

Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors…

Machine Learning · Computer Science 2025-09-29 Snir Hordan , Maya Bechler-Speicher , Gur Lifshitz , Nadav Dym

The study of Graph Neural Networks has received considerable interest in the past few years. By extending deep learning to graph-structured data, GNNs can solve a diverse set of tasks in fields including social science, chemistry, and…

Machine Learning · Computer Science 2024-03-12 Ashwin Nalwade , Kelly Marshall , Axel Eladi , Umang Sharma

Today we have a good theoretical understanding of the representational power of Graph Neural Networks (GNNs). For example, their limitations have been characterized in relation to a hierarchy of Weisfeiler-Lehman (WL) isomorphism tests.…

Machine Learning · Computer Science 2023-03-08 Mohammad Sadegh Akhondzadeh , Vijay Lingam , Aleksandar Bojchevski

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…

Machine Learning · Computer Science 2022-02-01 Cristian Bodnar , Fabrizio Frasca , Nina Otter , Yu Guang Wang , Pietro Liò , Guido Montúfar , Michael Bronstein

Various recent proposals increase the distinguishing power of Graph Neural Networks GNNs by propagating features between $k$-tuples of vertices. The distinguishing power of these "higher-order'' GNNs is known to be bounded by the…

Machine Learning · Computer Science 2021-06-15 Pablo Barceló , Floris Geerts , Juan Reutter , Maksimilian Ryschkov

Graph Neural Networks (GNNs) are widely used for graph representation learning in many application domains. The expressiveness of vanilla GNNs is upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL) test as they operate on rooted subtrees…

Machine Learning · Computer Science 2024-01-10 Jiaxing Xu , Aihu Zhang , Qingtian Bian , Vijay Prakash Dwivedi , Yiping Ke

Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on…

Machine Learning · Computer Science 2024-04-02 Quang Truong , Peter Chin

Graph Neural Networks (GNNs) have emerged as a powerful tool for data-driven learning on various graph domains. They are usually based on a message-passing mechanism and have gained increasing popularity for their intuitive formulation,…

Machine Learning · Computer Science 2023-11-02 Giuseppe Alessio D'Inverno , Simone Brugiapaglia , Mirco Ravanelli

The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension…

Discrete Mathematics · Computer Science 2019-04-16 Martin Grohe , Sandra Kiefer

The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared…

Machine Learning · Computer Science 2021-11-25 Chengxuan Ying , Tianle Cai , Shengjie Luo , Shuxin Zheng , Guolin Ke , Di He , Yanming Shen , Tie-Yan Liu