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Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks.
The strength of weak ties: A network theory revisited
Mark Granovetter · 1983
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Matrix perturbation theory
Gilbert W Stewart and Ji-guang Sun · 1990
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Spectral graph theory , volume 92
Fan RK Chung · 1997
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Community structure in social and biological networks
Michelle Girvan and Mark EJ Newman · 2002
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An efficient algorithm for detecting frequent subgraphs in biological networks
Mehmet Koyutürk, Ananth Grama, and Wojciech Szpankowski · 2004
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Finding frequent subgraphs in longitudinal social network data using a weighted graph mining approach
Chuntao Jiang, Frans Coenen, and Michele Zito · 2010
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Matrix analysis
Roger A Horn and Charles R Johnson · 2012
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Convolutional networks on graphs for learning molecular fingerprints
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A useful variant of the davis–kahan theorem for statisticians
Yi Yu, Tengyao Wang, and Richard J Samworth · 2015
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Spectrally-normalized margin bounds for neural networks
Peter L Bartlett, Dylan J Foster, and Matus J Telgarsky · 2017
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Geometric deep learning: going beyond euclidean data
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Parseval networks: Improving robustness to adversarial examples
Moustapha Cisse, Piotr Bojanowski, Edouard Grave, Yann Dauphin, and Nicolas Usunier · 2017
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Joint distribution optimal transportation for domain adaptation
Nicolas Courty, Rémi Flamary, Amaury Habrard, and Alain Rakotomamonjy · 2017
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Semi-supervised classification with graph convolutional networks
Thomas N Kipf and Max Welling · 2017
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Exploring generalization in deep learning
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nati Srebro · 2017
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Robust large margin deep neural networks
Jure Sokolić, Raja Giryes, Guillermo Sapiro, and Miguel RD Rodrigues · 2017
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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
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Deep sets
Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Russ R Salakhutdinov, and Alexander J Smola · 2017
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A PAC-bayesian approach to spectrally-normalized margin bounds for neural networks
Behnam Neyshabur, Srinadh Bhojanapalli, and Nathan Srebro · 2018
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Wasserstein distance guided representation learning for domain adaptation
Jian Shen, Yanru Qu, Weinan Zhang, and Yong Yu · 2018
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Lipschitz-margin training: Scalable certification of perturbation invariance for deep neural networks
Yusuke Tsuzuku, Issei Sato, and Masashi Sugiyama · 2018
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Link prediction based on graph neural networks
Muhan Zhang and Yixin Chen · 2018
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Alchemy: A quantum chemistry dataset for benchmarking ai models
Guangyong Chen, Pengfei Chen, Chang-Yu Hsieh, Chee-Kong Lee, Benben Liao, Renjie Liao, Weiwen Liu, Jiezhong Qiu, Qiming Sun, Jie Tang, Richard S. Zemel, and Shengyu Zhang · 2019
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Weisfeiler and leman go neural: Higher-order graph neural networks
Christopher Morris, Martin Ritzert, Matthias Fey, William L Hamilton, Jan Eric Lenssen, Gaurav Rattan, and Martin Grohe · 2019
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How powerful are graph neural networks?
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka · 2019
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How neural networks extrapolate: From feedforward to graph neural networks
K. Xu, M. Zhang, J. Li, S. Du, K. Kawarabayashi, and S. Jegelka · 2021
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Do transformers really perform badly for graph representation?
Chengxuan Ying, Tianle Cai, Shengjie Luo, Shuxin Zheng, Guolin Ke, Di He, Yanming Shen, and Tie-Yan Liu · 2021
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Identity-aware graph neural networks
Jiaxuan You, Jonathan M Gomes-Selman, Rex Ying, and Jure Leskovec · 2021
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Nested graph neural networks
Muhan Zhang and Pan Li · 2021
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Robust graph neural networks via probabilistic lipschitz constraints
Raghu Arghal, Eric Lei, and Shirin Saeedi Bidokhti · 2022
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Equivariant subgraph aggregation networks
Beatrice Bevilacqua, Fabrizio Frasca, Derek Lim, Balasubramaniam Srinivasan, Chen Cai, Gopinath Balamurugan, Michael M. Bronstein, and Haggai Maron · 2022
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Position-aware graph neural networks
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On weisfeiler-leman invariance: Subgraph counts and related graph properties
Vikraman Arvind, Frank Fuhlbrück, Johannes Köbler, and Oleg Verbitsky · 2020
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Can graph neural networks count substructures?
Zhengdao Chen, Lei Chen, Soledad Villar, and Joan Bruna · 2020
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Stability properties of graph neural networks
Fernando Gama, Joan Bruna, and Alejandro Ribeiro · 2020
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Generalization and representational limits of graph neural networks
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On the stability of polynomial spectral graph filters
Henry Kenlay, Dorina Thanou, and Xiaowen Dong · 2020
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Distance encoding: Design provably more powerful neural networks for graph representation learning
Pan Li, Yanbang Wang, Hongwei Wang, and Jure Leskovec · 2020
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Improving graph neural network expressivity via subgraph isomorphism counting
Giorgos Bouritsas, Fabrizio Frasca, Stefanos Zafeiriou, and Michael M Bronstein · 2022
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Tree mover’s distance: Bridging graph metrics and stability of graph neural networks
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Graph neural networks with learnable structural and positional representations
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Pure transformers are powerful graph learners
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Generalized laplacian positional encoding for graph representation learning
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Recipe for a general, powerful, scalable graph transformer
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From stars to subgraphs: Uplifting any GNN with local structure awareness
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Specformer: Spectral graph neural networks meet transformers
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Graph positional encoding via random feature propagation
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Sign and basis invariant networks for spectral graph representation learning
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WL meet VC
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