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In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data.
Provably powerful graph networks
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On Construction and Identification of Graphs
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The beacon set approach to graph isomorphism
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Lectures on graph isomorphism
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Probabilistic analysis of a canonical numbering algorithm for graphs
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Random graph isomorphism
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Practical graph isomorphism
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Distinguishing vertices of random graphs
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Partitioning a graph in O ( | A | log 2 | V | ) O(|A|\log_{2}|V|)
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Extended connectivity in chemical graphs
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DARC system: notions of defined and generic substructures. filiation and coding of FREL substructure (SS) classes
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Describing Graphs: A First-Order Approach to Graph Canonization , pages 59–81
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A graph reconstructor’s manual
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Approximation capabilities of multilayer feedforward networks
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A note on compact graphs
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Morgan revisited
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A graduated assignment algorithm for graph matching
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Representation theory and invariant neural networks
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A neural device for searching direct correlations between structures and properties of chemical compounds
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Bounded variable logics and counting – A study in finite models , volume 9 of Lecture Notes in Logic
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Supervised neural networks for the classification of structures
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Feature trees: A new molecular similarity measure based on tree matching
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Equivalence in finite-variable logics is complete for polynomial time
M. Grohe · 1999
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Convolution kernels on discrete structures
D. Haussler · 1999
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Approximation theory of the MLP model in neural networks
A. Pinkus · 1999
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Forestal algebras and algebraic forests (on a new class of weakly compact graphs)
S. Evdokimov, I. N. Ponomarenko, and G. Tinhofer · 2000
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Isomorphism testing for embeddable graphs through definability
M. Grohe · 2000
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Weisfeiler-Lehman refinement requires at least a linear number of iterations
M. Fürer · 2001
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Modern Graph Theory
B. Bollobás · 2002
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Reoptimization of MDL keys for use in drug discovery
J. L. Durant, B. A. L., D. R. Henry, and J. G. Nourse · 2002
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Network motifs: simple building blocks of complex networks
R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon · 2002
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On graph kernels: Hardness results and efficient alternatives
T. Gärtner, P. Flach, and S. Wrobel · 2003
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Marginalized kernels between labeled graphs
H. Kashima, K. Tsuda, and A. Inokuchi · 2003
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The structure and function of complex networks
M. E. J. Newman · 2003
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Graph complexity of chemical compounds in biological pathways
A. Yamaguchi, K. F. Aoki, and H. Mamitsuka · 2003
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Network biology: Understanding the cell’s functional organization
A.-L. Barabasi and Z. N. Oltvai · 2004
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Molecular similarity searching using atom environments, information-based feature selection, and a naïve bayesian classifier
A. Bender, H. Y. Mussa, R. C. Glen, and S. Reiling · 2004
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Locality-sensitive hashing scheme based on p p -stable distributions
M. Datar, N. Immorlica, P. Indyk, and V. S. Mirrokni · 2004
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Learning with distance substitution kernels
B. Haasdonk and C. Bahlmann · 2004
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Shortest-path kernels on graphs
K. M. Borgwardt and H.-P. Kriegel · 2005
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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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Optimal assignment kernels for attributed molecular graphs
H. Fröhlich, J. K. Wegner, F. Sieker, and A. Zell · 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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Graph kernels for chemical informatics
L. Ralaivola, S. J. Swamidass, H. Saigo, and P. Baldi · 2005
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Hierarchical inter-message passing for learning on molecular graphs
M. Fey, J. Yuen, and F. Weichert · 2006
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ErG: 2d pharmacophore descriptions for scaffold hopping
N. Stiefl, I. A. Watson, K. Baumann, and A. Zaliani · 2006
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TUDataset: A collection of benchmark datasets for learning with graphs
C. Morris, N. M. Kriege, F. Bause, K. Kersting, P. Mutzel, and M. Neumann · 2007
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Coordinate descent method for large-scale l2-loss linear support vector machines
K.-W. Chang, C.-J. Hsieh, and C.-J. Lin · 2008
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Improved random graph isomorphism
T. Czajka and G. Pandurangan · 2008
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Chemical information systems daylight, daylight theory manual v4.9
Daylight · 2008
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The optimal assignment kernel is not positive definite
J.-P. Vert · 2008
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Consistency of spectral clustering
U. von Luxburg, M. Belkin, and O. Bousquet · 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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Fast subtree kernels on graphs
N. Shervashidze and K. M. Borgwardt · 2009
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Efficient graphlet kernels for large graph comparison
N. Shervashidze, S. V. N. Vishwanathan, T. H. Petri, K. Mehlhorn, and K. M. Borgwardt · 2009
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Fast neighborhood subgraph pairwise distance kernel
F. Costa and K. De Grave · 2010
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On recognizing graphs by numbers of homomorphisms
Z. Dvorák · 2010
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Networks, Crowds, and Markets: Reasoning About a Highly Connected World
D. Easley and J. Kleinberg · 2010
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Frequent subgraph mining in outerplanar graphs
T. Horváth, J. Ramon, and S. Wrobel · 2010
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Extended-connectivity fingerprints
D. Rogers and M. Hahn · 2010
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Adaptive matching based kernels for labelled graphs
A. Woźnica, A. Kalousis, and M. Hilario · 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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Fixed-point definability and polynomial time on graphs with excluded minors
M. Grohe · 2012
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Fast random walk graph kernel
U. Kang, H. Tong, and J. Sun · 2012
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Subgraph matching kernels for attributed graphs
N. Kriege and P. Mutzel · 2012
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Foundations of Machine Learning
M. Mohri, A. Rostamizadeh, and A. Talwalkar · 2012
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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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Dimension reduction via colour refinement
M. Grohe, K. Kersting, M. Mladenov, and E. Selman · 2014
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A simple proof of the universality of invariant/equivariant graph neural networks
T. Maehara and H. NT · 2019
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Weisfeiler and leman go neural: Higher-order graph neural networks
C. Morris, M. Ritzert, M. Fey, W. L. Hamilton, J. E. Lenssen, G. Rattan, and M. Grohe · 2019
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Theoretical issues in deep networks: Approximation, optimization and generalization
T. A. Poggio, A. Banburski, and Q. Liao · 2019
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A persistent Weisfeiler-Lehman procedure for graph classification
B. Rieck, C. Bock, and K. M. Borgwardt · 2019
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Protein complex similarity based on Weisfeiler-Lehman labeling
B. K. Stöcker, T. Schäfer, P. Mutzel, J. Köster, N. M. Kriege, and S. Rahmann · 2019
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K. Kersting, M. Mladenov, R. Garnett, and M. Grohe · 2014
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Sherali–Adams relaxations of graph isomorphism polytopes
P. N. Malkin · 2014
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Hardness of robust graph isomorphism, Lasserre gaps, and asymmetry of random graphs
R. O’Donnell, J. Wright, C. Wu, and Y. Zhou · 2014
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Quantum chemistry structures and properties of 134 kilo molecules
R. Ramakrishnan, O. Dral, P., M. Rupp, and O. A. von Lilienfeld · 2014
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Understanding Machine Learning: From Theory to Algorithms
S. Shalev-Shwartz and S. Ben-David · 2014
Cited alongside, same era.
On the power of color refinement
V. Arvind, J. Köbler, G. Rattan, and O. Verbitsky · 2015
Cited alongside, same era.
Wasserstein weisfeiler-lehman graph kernels
M. Togninalli, E. Ghisu, F. Llinares-López, B. Rieck, and K. M. Borgwardt · 2019
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A functional representation for graph matching
F. Wang, N. Xue, Y. Zhang, G. Xia, and M. Pelillo · 2019
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How powerful are graph neural networks?
K. Xu, W. Hu, J. Leskovec, and S. Jegelka · 2019
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On the bottleneck of graph neural networks and its practical implications
U. Alon and E. Yahav · 2020
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Characterizing the expressive power of invariant and equivariant graph neural networks
W. Azizian and M. Lelarge · 2020
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Learning-based efficient graph similarity computation via multi-scale convolutional set matching
Y. Bai, H. Ding, K. Gu, Y. Sun, and W. Wang · 2020
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The logical expressiveness of graph neural networks
P. Barceló, E. V. Kostylev, M. Monet, J. Pérez, J. L. Reutter, and J. P. Silva · 2020
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D. Beaini, S. Passaro, V. Létourneau, W. L. Hamilton, G. Corso, and P. Liò · 2020
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Graph kernels: State-of-the-art and future challenges
K. M. Borgwardt, M. E. Ghisu, F. Llinares-López, L. O’Bray, and B. Rieck · 2020
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Machine learning on graphs: A model and comprehensive taxonomy
I. Chami, S. Abu-El-Haija, B. Perozzi, C. Ré, and K. Murphy · 2020
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Coloring graph neural networks for node disambiguation
G. Dasoulas, L. D. Santos, K. Scaman, and A. Virmaux · 2020
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Generalization and representational limits of graph neural networks
V. Garg, S. Jegelka, and T. Jaakkola · 2020
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The expressive power of kth-order invariant graph networks
F. Geerts · 2020
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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 · 2020
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Open graph benchmark: Datasets for machine learning on graphs
W. Hu, M. Fey, M. Zitnik, Y. Dong, H. Ren, B. Liu, M. Catasta, and J. Leskovec · 2020
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The iteration number of colour refinement
S. Kiefer and B. D. McKay · 2020
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Directional message passing for molecular graphs
J. Klicpera, J. Groß, and S. Günnemann · 2020
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A survey on graph kernels
N. M. Kriege, F. D. Johansson, and C. Morris · 2020
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Distance encoding: Design provably more powerful neural networks for graph representation learning
P. Li, Y. Wang, H. Wang, and J. Leskovec · 2020
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Towards deeper graph neural networks
M. Liu, H. Gao, and S. Ji · 2020
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On learning sets of symmetric elements
H. Maron, O. Litany, G. Chechik, and E. Fetaya · 2020
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Graph homomorphism convolution
H. NT and T. Maehara · 2020
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From graph low-rank global attention to 2-FWL approximation
O. Puny, H. Ben-Hamu, and Y. Lipman · 2020
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Ghashing: Semantic graph hashing for approximate similarity search in graph databases
Z. Qin, Y. Bai, and Y. Sun · 2020
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Universal equivariant multilayer perceptrons
S. Ravanbakhsh · 2020
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Random features strengthen graph neural networks
R. Sato, M. Yamada, and H. Kashima · 2020
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Graph neural networks for prediction of fuel ignition quality
A. M. Schweidtmann, J. G. Rittig, A. König, M. Grohe, A. Mitsos, and M. Dahmen · 2020
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On universal equivariant set networks
N. Segol and Y. Lipman · 2020
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A deep learning approach to antibiotic discovery
J. Stokes, K. Yang, K. Swanson, W. Jin, A. Cubillos-Ruiz, N. Donghia, C. MacNair, S. French, L. Carfrae, Z. Bloom-Ackerman, V. Tran, A. Chiappino-Pepe, A. Badran, I. Andrews, E. Chory, G. Church, E. Brown, T. Jaakkola, R. Barzilay, and J. Collins · 2020
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Building powerful and equivariant graph neural networks with structural message-passing
C. Vignac, A. Loukas, and P. Frossard · 2020
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A compact review of molecular property prediction with graph neural networks
O. Wieder, S. Kohlbacher, M. Kuenemann, A. Garon, P. Ducrot, T. Seidel, and T. Langer · 2020
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What can neural networks reason about?
K. Xu, J. Li, M. Zhang, S. S. Du, K. Kawarabayashi, and S. Jegelka · 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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Breaking the limits of message passing graph neural networks
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Graph neural networks with local graph parameters
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Equivariant subgraph aggregation networks
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On the sample complexity of learning under geometric stability
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Geometric deep learning: Grids, groups, graphs, geodesics, and gauges
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Reconstruction for powerful graph representations
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Provably strict generalisation benefit for equivariant models
B. Elesedy and S. Zaidi · 2021
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The logic of graph neural networks
M. Grohe · 2021
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Logarithmic Weisfeiler-Leman identifies all planar graphs
M. Grohe and S. Kiefer · 2021
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Recent advances on the graph isomorphism problem
M. Grohe and D. Neuen · 2021
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A survey of topological machine learning methods
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Highly accurate protein structure prediction with AlphaFold
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Implicit MLE: backpropagating through discrete exponential family distributions
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From stars to subgraphs: Uplifting any GNN with local structure awareness
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Exponentially improving the complexity of simulating the Weisfeiler-Lehman test with graph neural networks
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Two-dimensional Weisfeiler-Lehman graph neural networks for link prediction
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Weisfeiler and Leman go walking: Random walk kernels revisited
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