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Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the $1$-dimensional Weisfeiler--Leman algorithm ($1\text{-}\mathsf{WL}$).
The reduction of a graph to canonical form and the algebra which appears therein
B. Weisfeiler and A. Leman · 1968
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On Construction and Identification of Graphs
B. Weisfeiler · 1976
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Lectures on graph isomorphism
L. Babai · 1979
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Canonical labelling of graphs in linear average time
L. Babai and L. Kucera · 1979
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Describing graphs: A first-order approach to graph canonization
N. Immerman and E. Lander · 1990
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An optimal lower bound on the number of variables for graph identifications
J. Cai, M. Fürer, and N. Immerman · 1992
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Chemnet: A novel neural network based method for graph/property mapping
D. B. Kireev · 1995
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The Nature of Statistical Learning Theory
V. N. Vapnik · 1995
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Learning task-dependent distributed representations by backpropagation through structure
C. Goller and A. Küchler · 1996
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A neural device for searching direct correlations between structures and properties of chemical compounds
I. I. Baskin, V. A. Palyulin, and N. S. Zefirov · 1997
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Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks
M. Karpinski and A. Macintyre · 1997
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Supervised neural networks for the classification of structures
A. Sperduti and A. Starita · 1997
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Network biology: Understanding the cell’s functional organization
A.-L. Barabasi and Z. N. Oltvai · 2004
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Brenda, the enzyme database: updates and major new developments
I. Schomburg, A. Chang, C. Ebeling, M. Gremse, C. Heldt, G. Huhn, and D. Schomburg · 2004
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Protein function prediction via graph kernels
K. M. Borgwardt, C. S. Ong, S. Schönauer, S. V. N. Vishwanathan, A. J. Smola, and H.-P. Kriegel · 2005
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Derivation and validation of toxicophores for mutagenicity prediction
J. Kazius, R. McGuire, and R. Bursi · 2005
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Automatic generation of complementary descriptors with molecular graph networks
C. Merkwirth and T. Lengauer · 2005
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A new neural network model for contextual processing of graphs
A. Micheli and A. S. Sestito · 2005
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Transductive rademacher complexity and its applications
R. El-Yaniv and D. Pechyony · 2007
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IAM graph database repository for graph based pattern recognition and machine learning
K. Riesen and H. Bunke · 2008
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Comparison of descriptor spaces for chemical compound retrieval and classification
N. Wale, I. A. Watson, and G. Karypis · 2008
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Mining significant graph patterns by leap search
X. Yan, H. Cheng, J. Han, and P. S. Yu · 2008
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Neural network for graphs: A contextual constructive approach
A. Micheli · 2009
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The graph neural network model
F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini · 2009
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Networks, Crowds, and Markets: Reasoning About a Highly Connected World
D. Easley and J. Kleinberg · 2010
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Introduction to testing graph properties
O. Goldreich · 2010
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Weisfeiler-Lehman graph kernels
N. Shervashidze, P. Schweitzer, E. J. van Leeuwen, K. Mehlhorn, and K. M. Borgwardt · 2011
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Sherali-adams relaxations and indistinguishability in counting logics
A. Atserias and E. N. Maneva · 2013
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Spectral networks and deep locally connected networks on graphs
J. Bruna, W. Zaremba, A. Szlam, and Y. LeCun · 2014
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Sherali–Adams relaxations of graph isomorphism polytopes
P. N. Malkin · 2014
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On the power of color refinement
V. Arvind, J. Köbler, G. Rattan, and O. Verbitsky · 2015
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Convolutional networks on graphs for learning molecular fingerprints
D. Duvenaud, D. Maclaurin, J. Aguilera-Iparraguirre, R. Gómez-Bombarelli, T. Hirzel, A. Aspuru-Guzik, and R. P. Adams · 2015
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Pebble games and linear equations
M. Grohe and M. Otto · 2015
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
S. Ioffe and C. Szegedy · 2015
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Graphs identified by logics with counting
S. Kiefer, P. Schweitzer, and E. Selman · 2015
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Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2015
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Graph isomorphism in quasipolynomial time
L. Babai · 2016
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Convolutional neural networks on graphs with fast localized spectral filtering
M. Defferrard, X. Bresson, and P. Vandergheynst · 2016
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Upper bounds on the quantifier depth for graph differentiation in first-order logic
S. Kiefer and P. Schweitzer · 2016
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Minimax lower bounds for realizable transductive classification
I. O. Tolstikhin and D. Lopez-Paz · 2016
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Tight lower and upper bounds for the complexity of canonical colour refinement
C. Berkholz, P. S. Bonsma, and M. Grohe · 2017
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On the combinatorial power of the Weisfeiler-Lehman algorithm
M. Fürer · 2017
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Neural message passing for quantum chemistry
J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl · 2017
Cited alongside, same era.
Descriptive Complexity, Canonisation, and Definable Graph Structure Theory
M. Grohe · 2017
Cited alongside, same era.
Inductive representation learning on large graphs
W. L. Hamilton, Z. Ying, and J. Leskovec · 2017
Cited alongside, same era.
Semi-supervised classification with graph convolutional networks
T. N. Kipf and M. Welling · 2017
Cited alongside, same era.
Geometric deep learning on graphs and manifolds using mixture model cnns
F. Monti, D. Boscaini, J. Masci, E. Rodolà, J. Svoboda, and M. M. Bronstein · 2017
Cited alongside, same era.
Dynamic edge-conditioned filters in convolutional neural networks on graphs
M. Simonovsky and N. Komodakis · 2017
Cited alongside, same era.
Building powerful and equivariant graph neural networks with structural message-passing
C. Vignac, A. Loukas, and P. Frossard · 2020
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The surprising power of graph neural networks with random node initialization
R. Abboud, İ. İ. Ceylan, M. Grohe, and T. Lukasiewicz · 2021
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Characterizing the expressive power of invariant and equivariant graph neural networks
W. Azizian and M. Lelarge · 2021
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Breaking the limits of message passing graph neural networks
M. Balcilar, P. Héroux, B. Gaüzère, P. Vasseur, S. Adam, and P. Honeine · 2021
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Graph neural networks with local graph parameters
P. Barceló, F. Geerts, J. L. Reutter, and M. Ryschkov · 2021
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Directional graph networks
D. Beaini, S. Passaro, V. Létourneau, W. L. Hamilton, G. Corso, and P. Lió · 2021
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Lovász meets Weisfeiler and Leman
H. Dell, M. Grohe, and G. Rattan · 2018
Cited alongside, same era.
A property testing framework for the theoretical expressivity of graph kernels
N. M. Kriege, C. Morris, A. Rey, and C. Sohler · 2018
Cited alongside, same era.
Foundations of Machine Learning
M. Mohri, A. Rostamizadeh, and A. Talwalkar · 2018
Cited alongside, same era.
The Vapnik-Chervonenkis dimension of graph and recursive neural networks
F. Scarselli, A. C. Tsoi, and M. Hagenbuchner · 2018
Cited alongside, same era.
Graph attention networks
P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Liò, and Y. Bengio · 2018
Cited alongside, same era.
Representation learning on graphs with jumping knowledge networks
K. Xu, C. Li, Y. Tian, T. Sonobe, K. Kawarabayashi, and S. Jegelka · 2018
Cited alongside, same era.
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Reconstruction for powerful graph representations
L. Cotta, C. Morris, and B. Ribeiro · 2021
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Learning theory can (sometimes) explain generalisation in graph neural networks
P. M. Esser, L. C. Vankadara, and D. Ghoshdastidar · 2021
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Let’s agree to degree: Comparing graph convolutional networks in the message-passing framework
F. Geerts, F. Mazowiecki, and G. A. Pérez · 2021
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The logic of graph neural networks
M. Grohe · 2021
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Highly accurate protein structure prediction with AlphaFold
J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. Žídek, A. Potapenko, A. Bridgland, C. Meyer, S. A. A. Kohl, A. J. Ballard, A. Cowie, B. Romera-Paredes, S. Nikolov, R. Jain, J. Adler, T. Back, S. Petersen, D. Reiman, E. Clancy, M. Zielinski, M. Steinegger, M. Pacholska, T. Berghammer, S. Bodenstein, D. Silver, O. Vinyals, A. W. Senior, K. Kavukcuoglu, P. Kohli, and D. Hassabis · 2021
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A PAC-Bayesian approach to generalization bounds for graph neural networks
R. Liao, R. Urtasun, and R. S. Zemel · 2021
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Weisfeiler and Leman go machine learning: The story so far
C. Morris, Y. L., H. Maron, B. Rieck, N. M. Kriege, M. Grohe, M. Fey, and K. Borgwardt · 2021
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DropGNN: Random dropouts increase the expressiveness of graph neural networks
P. A. Papp, L. F. K. Martinkus, and R. Wattenhofer · 2021
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Random features strengthen graph neural networks
R. Sato, M. Yamada, and H. Kashima · 2021
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Neural trees for learning on graphs
R. Talak, S. Hu, L. Peng, and L. Carlone · 2021
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Autobahn: Automorphism-based graph neural nets
E. H. Thiede, W. Zhou, and R. Kondor · 2021
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Graph learning with 1D convolutions on random walks
J. Tönshoff, M. Ritzert, H. Wolf, and M. Grohe · 2021
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From local structures to size generalization in graph neural networks
G. Yehudai, E. Fetaya, E. A. Meirom, G. Chechik, and H. Maron · 2021
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Identity-aware graph neural networks
J. You, J. Gomes-Selman, R. Ying, and J. Leskovec · 2021
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Nested graph neural networks
M. Zhang and P. Li · 2021
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Exponentially improving the complexity of simulating the Weisfeiler-Lehman test with graph neural networks
A. Aamand, J. Y. Chen, P. Indyk, S. Narayanan, R. Rubinfeld, N. Schiefer, S. Silwal, and T. Wagner · 2022
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Weisfeiler and leman go relational
P. Barceló, M. Galkin, C. Morris, and M. A. R. Orth · 2022
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Equivariant subgraph aggregation networks
B. Bevilacqua, F. Frasca, D. Lim, B. Srinivasan, C. Cai, G. Balamurugan, M. M. Bronstein, and H. Maron · 2022
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How powerful are k-hop message passing graph neural networks
J. Feng, Y. Chen, F. Li, A. Sarkar, and M. Zhang · 2022
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Understanding and extending subgraph GNNs by rethinking their symmetries
F. Frasca, B. Bevilacqua, M. M. Bronstein, and H. Maron · 2022
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Expressiveness and approximation properties of graph neural networks
F. Geerts and J. L. Reutter · 2022
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Topological graph neural networks
M. Horn, E. D. Brouwer, M. Moor, Y. Moreau, B. Rieck, and K. M. Borgwardt · 2022
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Boosting the cycle counting power of graph neural networks with I 2 {}^{\mbox{2}} -GNNs
Y. Huang, X. Peng, J. Ma, and M. Zhang · 2022
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Pure transformers are powerful graph learners
J. Kim, T. D. Nguyen, S. Min, S. Cho, M. Lee, H. Lee, and S. Hong · 2022
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Agent-based graph neural networks
K. Martinkus, P. A. Papp, B. Schesch, and R. Wattenhofer · 2022
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Generalization analysis of message passing neural networks on large random graphs
S. Maskey, Y. Lee, R. Levie, and G. Kutyniok · 2022
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SpeqNets: Sparsity-aware permutation-equivariant graph networks
C. Morris, G. Rattan, S. Kiefer, and S. Ravanbakhsh · 2022
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A theoretical comparison of graph neural network extensions
P. A. Papp and R. Wattenhofer · 2022
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Ordered subgraph aggregation networks
C. Qian, G. Rattan, F. Geerts, C. Morris, and M. Niepert · 2022
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A new perspective on "how graph neural networks go beyond weisfeiler-lehman?"
A. Wijesinghe and Q. Wang · 2022
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From stars to subgraphs: Uplifting any GNN with local structure awareness
L. Zhao, W. Jin, L. Akoglu, and N. Shah · 2022
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The descriptive complexity of graph neural networks
M. Grohe · 2023
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Generalization in graph neural networks: Improved pac-bayesian bounds on graph diffusion
H. Ju, D. Li, A. Sharma, and H. R. Zhang · 2023
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Attending to graph transformers
L. Müller, M. Galkin, C. Morris, and L. Rampásek · 2023
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Equivariant polynomials for graph neural networks
O. Puny, D. Lim, B. T. Kiani, H. Maron, and Y. Lipman · 2023
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Some might say all you need is sum
E. Rosenbluth, J. Tönshoff, and M. Grohe · 2023
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