mlsanityData to 7 Oct 2026

Elastic Graph Neural Networks

arXiv 2107.06996 ↗First posted 5 Jul 2021cs.LG cs.AI cs.NEcited by 67

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Abstract (arXiv)

While many existing graph neural networks (GNNs) have been proven to perform ℓ2-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via ℓ1-based graph smoothing. As a result, we introduce a family of GNNs (Elastic GNNs) based on ℓ1 and ℓ2-based graph smoothing. In particular, we propose a novel and general message passing scheme into GNNs. This message passing algorithm is not only friendly to back-propagation training but also achieves the desired smoothing properties with a theoretical convergence guarantee. Experiments on semi-supervised learning tasks demonstrate that the proposed Elastic GNNs obtain better adaptivity on benchmark datasets and are significantly robust to graph adversarial attacks. The implementation of Elastic GNNs is available at urlhttps://github.com/lxiaorui/ElasticGNN.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). Builds on 25 of its 50 references that are in the map. First posted on arXiv 5 Jul 2021.

Builds on

25 of 50 references.

References · 25

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2017Inductive Representation Learning on Large Graphscited by 6,284
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  7. 2019Simplifying Graph Convolutional Networkscited by 1,470
  8. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  9. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  10. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 395
  11. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 368
  12. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
13 more
  1. 2019Adversarial Attacks on Graph Neural Networks via Meta Learningcited by 261
  2. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  3. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  4. 2020A Unified View on Graph Neural Networks as Graph Signal Denoisingcited by 110
  5. 2020DeepRobust: A PyTorch Library for Adversarial Attacks and Defensescited by 78
  6. 2013Adaptive piecewise polynomial estimation via trend filteringcited by 47
  7. 2014Trend Filtering on Graphscited by 45
  8. 2020Graph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoisingcited by 33
  9. 2019Vector-Valued Graph Trend Filtering with Non-Convex Penaltiescited by 12
  10. 2019Semi-supervised Learning in Network-Structured Data via Total Variation Minimizationcited by 10
  11. 2013Multiclass Total Variation Clusteringcited by 7
  12. 2013An Adaptive Total Variation Algorithm for Computing the Balanced Cut of a Graphcited by 2
  13. 2017New convergence analysis of a primal-dual algorithm with large stepsizescited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 28; 2023: 19; 2024: 10; 2025: 3; 2026: 2.

67 papers.

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  1. 2021Graph Condensation for Graph Neural Networkscited by 150
  2. 2022Condensing Graphs via One-Step Gradient Matchingcited by 100
  3. 2022A Survey on Graph Representation Learning Methodscited by 66
  4. 2023Cluster-guided Contrastive Graph Clustering Networkcited by 60
  5. 2021Graph Trend Filtering Networks for Recommendationscited by 53
  6. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
  7. 2022Linkless Link Prediction via Relational Distillationcited by 39
  8. 2023Are Defenses for Graph Neural Networks Robust?cited by 38
  9. 2022FMP: Toward Fair Graph Message Passing against Topology Biascited by 35
  10. 2022Reliable Representations Make A Stronger Defender: Unsupervised Structure Refinement for Robust GNNcited by 34
  11. 2024A Review of Graph Neural Networks in Epidemic Modelingcited by 31
  12. 2022Optimization-Induced Graph Implicit Nonlinear Diffusioncited by 28
38 more
  1. 2022Transformers from an Optimization Perspectivecited by 27
  2. 2022A Survey of Trustworthy Graph Learning: Reliability, Explainability, and Privacy Protectioncited by 20
  3. 2022Feature Overcorrelation in Deep Graph Neural Networks: A New Perspectivecited by 19
  4. 2021Jointly Attacking Graph Neural Network and its Explanationscited by 18
  5. 2022Test-Time Training for Graph Neural Networkscited by 17
  6. 2023From Hypergraph Energy Functions to Hypergraph Neural Networkscited by 17
  7. 2022Defending Graph Convolutional Networks against Dynamic Graph Perturbations via Bayesian Self-supervisioncited by 16
  8. 2023LazyGNN: Large-Scale Graph Neural Networks via Lazy Propagationcited by 16
  9. 2023A Unified Framework of Graph Information Bottleneck for Robustness and Membership Privacycited by 14
  10. 2021Implicit vs Unfolded Graph Neural Networkscited by 12
  11. 2022Robust Node Classification on Graphs: Jointly from Bayesian Label Transition and Topology-based Label Propagationcited by 12
  12. 2023Chasing Fairness in Graphs: A GNN Architecture Perspectivecited by 12
  13. 2022Recent Advances in Reliable Deep Graph Learning: Inherent Noise, Distribution Shift, and Adversarial Attackcited by 10
  14. 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attackscited by 9
  15. 2021Graph Denoising with Framelet Regularizercited by 8
  16. 2022MGNN: Graph Neural Networks Inspired by Distance Geometry Problemcited by 8
  17. 2023Robust Graph Neural Networks via Unbiased Aggregationcited by 8
  18. 2022FocusedCleaner: Sanitizing Poisoned Graphs for Robust GNN-based Node Classificationcited by 7
  19. 2022Total Variation Graph Neural Networkscited by 7
  20. 2022Robust Graph Representation Learning for Local Corruption Recoverycited by 6
  21. 2023Efficient Link Prediction via GNN Layers Induced by Negative Samplingcited by 6
  22. 2024Minimum Topology Attacks for Graph Neural Networkscited by 6
  23. 2023Low-bit Quantization for Deep Graph Neural Networks with Smoothness-aware Message Propagationcited by 5
  24. 2024L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classificationcited by 5
  25. 2024Provable Robustness of (Graph) Neural Networks Against Data Poisoning and Backdoor Attackscited by 5
  26. 2022Alternately Optimized Graph Neural Networkscited by 4
  27. 2023IDEA: Invariant Defense for Graph Adversarial Robustnesscited by 4
  28. 2023Robust Node Representation Learning via Graph Variational Diffusion Networkscited by 4
  29. 2022Representation Power of Graph Neural Networks: Improved Expressivity via Algebraic Analysiscited by 3
  30. 2022Ensemble Multi-Relational Graph Neural Networkscited by 3
  31. 2023Generative Flow Networks for Precise Reward-Oriented Active Learning on Graphscited by 3
  32. 2023Towards Label Position Bias in Graph Neural Networkscited by 3
  33. 2022GUARD: Graph Universal Adversarial Defensecited by 2
  34. 2022Towards Understanding Graph Neural Networks: An Algorithm Unrolling Perspectivecited by 2
  35. 2023Graph Agent Network: Empowering Nodes with Inference Capabilities for Adversarial Resiliencecited by 2
  36. 2023Efficient Low-Rank GNN Defense Against Structural Attackscited by 2
  37. 2023Towards Inductive Robustness: Distilling and Fostering Wave-induced Resonance in Transductive GCNs Against Graph Adversarial Attackscited by 2
  38. 2024Are Your Models Still Fair? Fairness Attacks on Graph Neural Networks via Node Injectionscited by 2

50 most cited of 67 All 67 (JSON)