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Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks [article]

Christopher Morris, Martin Ritzert, Matthias Fey, William L. Hamilton, Jan Eric Lenssen, Gaurav Rattan, Martin Grohe
2021 arXiv   pre-print
These higher-order structures play an essential role in the characterization of social networks and molecule graphs.  ...  In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion.  ...  Analysis, projects A6 and B2.  ... 
arXiv:1810.02244v5 fatcat:jod7duiubfa7nc5bgiwhpukhpm

Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks

Christopher Morris, Martin Ritzert, Matthias Fey, William L. Hamilton, Jan Eric Lenssen, Gaurav Rattan, Martin Grohe
These higher-order structures play an essential role in the characterization of social networks and molecule graphs.  ...  In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion.  ...  Analysis, projects A6 and B2.  ... 
doi:10.1609/aaai.v33i01.33014602 fatcat:3ml3ojoi4rekddw2dy4mgvgxjq

Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings [article]

Or Feldman, Amit Boyarski, Shai Feldman, Dani Kogan, Avi Mendelson, Chaim Baskin
2022 arXiv   pre-print
This drawback hinders the applicability of Message Passing Graph Neural Networks (MPGNNs), whose expressive power is upper bounded by the WL test.  ...  Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the Weisfeiler-Leman (WL) test) and spectral invariants.  ...  Acknowledgements This research was partially supported by the Technion Hiroshi Fujiwara Cyber Security Research Center and the Israel National Cyber Directorate.  ... 
arXiv:2201.13410v2 fatcat:nqvzk544szd4zhpdtikavrkj3a

Weisfeiler and Leman go Machine Learning: The Story so far [article]

Christopher Morris, Yaron Lipman, Haggai Maron, Bastian Rieck, Nils M. Kriege, Martin Grohe, Matthias Fey, Karsten Borgwardt
2021 arXiv   pre-print
In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, emerged as a powerful tool for machine learning with  ...  graphs and relational data.  ...  Kriege is funded by the Vienna Science and Technology Fund (WWTF) through project VRG19-009.  ... 
arXiv:2112.09992v1 fatcat:r5ahhxsvhrbotfi6grerkzxuui

Counting Substructures with Higher-Order Graph Neural Networks: Possibility and Impossibility Results [article]

Behrooz Tahmasebi, Derek Lim, Stefanie Jegelka
2021 arXiv   pre-print
While message passing Graph Neural Networks (GNNs) have become increasingly popular architectures for learning with graphs, recent works have revealed important shortcomings in their expressive power.  ...  In response, several higher-order GNNs have been proposed that substantially increase the expressive power, albeit at a large computational cost.  ...  Higher-order networks use an encoding of k-tuples and then apply message passing [10] , or equivariant tensor operations [18] .  ... 
arXiv:2012.03174v2 fatcat:hdko7yf7g5af3krmyoj72ovfxm

The Logic of Graph Neural Networks [article]

Martin Grohe
2022 arXiv   pre-print
Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs.  ...  It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms and by finite variable counting logics.  ...  WEISFEILER AND LEMAN GO NEURAL In this section, we shall prove that GNNs have exactly the same expressiveness as colour refinement when it comes to distinguishing graphs or their vertices.  ... 
arXiv:2104.14624v2 fatcat:pkq6yfm53bfwxjznoxeegchzwi

Local Permutation Equivariance For Graph Neural Networks [article]

Joshua Mitton, Roderick Murray-Smith
2022 arXiv   pre-print
In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using permutation  ...  Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into  ...  Roderick Murray-Smith is grateful for EPSRC support through grants EP/R018634/1 and EP/T00097X/1.  ... 
arXiv:2111.11840v2 fatcat:6xaou6m2kvdi7mp62o4uxrryia

The Impact of Global Structural Information in Graph Neural Networks Applications [article]

Davide Buffelli, Fabio Vandin
2021 arXiv   pre-print
Graph Neural Networks (GNNs) rely on the graph structure to define an aggregation strategy where each node updates its representation by combining information from its neighbours.  ...  Therefore, practical GNN models employ few layers and only leverage the graph structure in terms of limited, small neighbourhoods around each node.  ...  Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks. AAAI, 2019. 10. Page, L.; Brin, S.; Motwani, R.; Winograd, T. The PageRank citation ranking: Bringing order to the Web.  ... 
arXiv:2006.03814v2 fatcat:xxm7fqiwtvbrjjxl5yoxctvs5q

Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting [article]

Giorgos Bouritsas, Fabrizio Frasca, Stefanos Zafeiriou, Michael M. Bronstein
2021 arXiv   pre-print
It has been shown that the expressive power of standard GNNs is bounded by the Weisfeiler-Leman (WL) graph isomorphism test, from which they inherit proven limitations such as the inability to detect and  ...  While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying  ...  Acknowledgements This research was partially supported by the ERC Consolidator Grant No. 724228 -LEMAN (GB and MB).  ... 
arXiv:2006.09252v3 fatcat:2a3zatznsvdkjkan4fm2zqtute

k-hop Graph Neural Networks [article]

Giannis Nikolentzos, George Dasoulas, Michalis Vazirgiannis
2020 arXiv   pre-print
Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations.  ...  Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of distinguishing non-isomorphic graphs.  ...  k-hop Graph Neural Networks In this section, we propose a generalization of GNNs, so-called k-hop Graph Neural Networks (k-hop GNNs).  ... 
arXiv:1907.06051v2 fatcat:7aj3dn5wljdghf72eja6whpnga

The Surprising Power of Graph Neural Networks with Random Node Initialization [article]

Ralph Abboud, İsmail İlkan Ceylan, Martin Grohe, Thomas Lukasiewicz
2021 arXiv   pre-print
Graph neural networks (GNNs) are effective models for representation learning on relational data.  ...  However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman graph isomorphism heuristic.  ...  Acknowledgments This work was supported by the Alan Turing Institute under the UK EPSRC grant EP/N510129/1, by the AXA Research Fund, and by the EPSRC grants EP/R013667/1 and EP/M025268/1.  ... 
arXiv:2010.01179v2 fatcat:qpi7idrhdbbc5ialjwllvgxwbi

On Graph Neural Networks versus Graph-Augmented MLPs [article]

Lei Chen, Zhengdao Chen, Joan Bruna
2020 arXiv   pre-print
From the perspective of expressive power, this work compares multi-layer Graph Neural Networks (GNNs) with a simplified alternative that we call Graph-Augmented Multi-Layer Perceptrons (GA-MLPs), which  ...  first augments node features with certain multi-hop operators on the graph and then applies an MLP in a node-wise fashion.  ...  Bronstein and Shunwang Gong for helpful conversations. This work is partially supported by the Alfred P.  ... 
arXiv:2010.15116v2 fatcat:zdiirbcuevhrvkei6kpakuaro4

RaWaNet: Enriching Graph Neural Network Input via Random Walks on Graphs [article]

Anahita Iravanizad, Edgar Ivan Sanchez Medina, Martin Stoll
2021 arXiv   pre-print
In recent years, graph neural networks (GNNs) have gained increasing popularity and have shown very promising results for data that are represented by graphs.  ...  Namely, (regular) walks of length 1 and 2, and a fractional walk of length γ∈ (0,1), in order to capture the different local and global dynamics on the graphs.  ...  They defined a local and global neighborhood for their introduced higher dimensional graph, which is based on higher order Weisfeiler-Leman graph isomorphisms.  ... 
arXiv:2109.07555v3 fatcat:xnx5yerrcnbe5kuxw5gzbzf6sq

Efficient Colon Cancer Grading with Graph Neural Networks [article]

Franziska Lippoldt
2020 arXiv   pre-print
The graph neural network itself consists of three convolutional blocks and linear layers, which is a rather simple design compared to other networks for this application.  ...  Further, the graph size in terms of nodes becomes stable with respect to the model's prediction and accuracy for sufficiently large models.  ...  References Ruqayya Awan, Korsuk Sirinukunwattana, David Epstein, Samuel Jefferyes, Uvais Qidwai, Zia Aftab, Imaad Mujeeb, David Snead, and Nasir Rajpoot.  ... 
arXiv:2010.01091v1 fatcat:hq72sxdh7ravpmzby7777cqvbq

Graph Neural Networks: Taxonomy, Advances and Trends [article]

Yu Zhou, Haixia Zheng, Xin Huang, Shufeng Hao, Dengao Li, Jumin Zhao
2022 arXiv   pre-print
In order to drive the graph neural networks into a new stage, we summarize four future research directions so as to overcome the facing challenges.  ...  First of all, we provide a novel taxonomy for the graph neural networks, and then refer to up to 400 relevant literatures to show the panorama of the graph neural networks.  ...  Specifically, they take higher-order graph structures at multiple scales into consideration by leveraging the k-Weisfeiler-Leman (k-WL) graph isomorphism test so that the message passing is performed directly  ... 
arXiv:2012.08752v3 fatcat:xj2kambrabfj3g5ldenfyixzu4
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