mlsanityData to 14 Oct 2026

Certifiable Robustness to Graph Perturbations

arXiv 1910.14356 ↗First posted 31 Oct 2019cs.LG cs.CR cs.SIcited by 62

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Abstract (arXiv)

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks on both the graph structure and the node attributes. We propose the first method for verifying certifiable (non-)robustness to graph perturbations for a general class of models that includes graph neural networks and label/feature propagation. By exploiting connections to PageRank and Markov decision processes our certificates can be efficiently (and under many threat models exactly) computed. Furthermore, we investigate robust training procedures that increase the number of certifiably robust nodes while maintaining or improving the clean predictive accuracy.

Key facts. Cited by 62 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Oct 2019.

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Citing papers per year: 2021: 15; 2022: 12; 2023: 14; 2024: 13; 2025: 7; 2026: 1.

62 papers.

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  1. 2022A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainabilitycited by 118
  2. 2021Robustness of Graph Neural Networks at Scalecited by 100
  3. 2022Trustworthy Graph Neural Networks: Aspects, Methods and Trendscited by 89
  4. 2021Robust Counterfactual Explanations on Graph Neural Networkscited by 72
  5. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  6. 2021Transferability of Graph Neural Networks: an Extended Graphon Approachcited by 53
  7. 2021Model Stealing Attacks Against Inductive Graph Neural Networkscited by 50
  8. 2021Single Node Injection Attack against Graph Neural Networkscited by 45
  9. 2021Understanding Structural Vulnerability in Graph Convolutional Networkscited by 37
  10. 2023SE-GSL: A General and Effective Graph Structure Learning Framework through Structural Entropy Optimizationcited by 35
  11. 2021Interpretable Stability Bounds for Spectral Graph Filterscited by 28
  12. 2023Adversarial Training for Graph Neural Networks: Pitfalls, Solutions, and New Directionscited by 28
38 more
  1. 2022Model Inversion Attacks against Graph Neural Networkscited by 26
  2. 2024Uncertainty in Graph Neural Networks: A Surveycited by 23
  3. 2023Data-centric Graph Learning: A Surveycited by 22
  4. 2021How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implicationscited by 21
  5. 2022Scalable Verification of GNN-based Job Schedulerscited by 19
  6. 2021Decentralized Inference with Graph Neural Networks in Wireless Communication Systemscited by 18
  7. 2021Stability of Graph Convolutional Neural Networks to Stochastic Perturbationscited by 18
  8. 2023Collective Robustness Certificates: Exploiting Interdependence in Graph Neural Networkscited by 16
  9. 2024A Simple and Yet Fairly Effective Defense for Graph Neural Networkscited by 12
  10. 2024Safety in Graph Machine Learning: Threats and Safeguardscited by 11
  11. 2022Localized Randomized Smoothing for Collective Robustness Certificationcited by 10
  12. 2023Randomized Message-Interception Smoothing: Gray-box Certificates for Graph Neural Networkscited by 10
  13. 2024Verifying message-passing neural networks via topology-based bounds tighteningcited by 10
  14. 2022A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunitiescited by 9
  15. 2023Hierarchical Randomized Smoothingcited by 9
  16. 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attackscited by 9
  17. 2021GraphAttacker: A General Multi-Task GraphAttack Frameworkcited by 8
  18. 2023Robust Graph Neural Networks via Unbiased Aggregationcited by 8
  19. 2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structurecited by 8
  20. 2022Neighboring Backdoor Attacks on Graph Convolutional Networkcited by 7
  21. 2024AttackGNN: Red-Teaming GNNs in Hardware Security Using Reinforcement Learningcited by 6
  22. 2022Robust Graph Representation Learning via Predictive Codingcited by 5
  23. 2023Certifiably Robust Graph Contrastive Learningcited by 5
  24. 2024Provable Robustness of (Graph) Neural Networks Against Data Poisoning and Backdoor Attackscited by 5
  25. 2023IDEA: Invariant Defense for Graph Adversarial Robustnesscited by 4
  26. 2024Generating Robust Counterfactual Witnesses for Graph Neural Networkscited by 4
  27. 2025Exact Verification of Graph Neural Networks with Incremental Constraint Solvingcited by 4
  28. 2024Faithful Interpretation for Graph Neural Networkscited by 3
  29. 2022GUARD: Graph Universal Adversarial Defensecited by 2
  30. 2022AdvCat: Domain-Agnostic Robustness Assessment for Cybersecurity-Critical Applications with Categorical Inputscited by 2
  31. 2023Graph Adversarial Immunization for Certifiable Robustnesscited by 2
  32. 2023Structure-Aware Robustness Certificates for Graph Classificationcited by 2
  33. 2023On the Robustness of Post-hoc GNN Explainers to Label Noisecited by 2
  34. 2023On the Trade-Off between Stability and Representational Capacity in Graph Neural Networkscited by 2
  35. 2024A Benchmark for Fairness-Aware Graph Learningcited by 2
  36. 2024A Cognac Shot To Forget Bad Memories: Corrective Unlearning for Graph Neural Networkscited by 2
  37. 2021Graphfool: Targeted Label Adversarial Attack on Graph Embeddingcited by 1
  38. 2021Adversarial Robustness of Probabilistic Network Embedding for Link Predictioncited by 1

50 most cited of 62 All 62 (JSON)