mlsanityData to 13 Oct 2026

Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach

arXiv 2310.06396 ↗First posted 10 Oct 2023cs.LGcited by 24

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Abstract (arXiv)

Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection to various stability notions such as BIBO stability, Lyapunov stability, structural stability, and conservative stability. We argue that Lyapunov stability, despite its common use, does not necessarily ensure adversarial robustness. Inspired by physics principles, we advocate for the use of conservative Hamiltonian neural flows to construct GNNs that are robust to adversarial attacks. The adversarial robustness of different neural flow GNNs is empirically compared on several benchmark datasets under a variety of adversarial attacks. Extensive numerical experiments demonstrate that GNNs leveraging conservative Hamiltonian flows with Lyapunov stability substantially improve robustness against adversarial perturbations. The implementation code of experiments is available at https://github.com/zknus/NeurIPS-2023-HANG-Robustness.

Key facts. Cited by 24 papers in the map (data through 13 Oct 2026). Builds on 53 of its 93 references that are in the map. First posted on arXiv 10 Oct 2023.

Builds on

53 of 93 references.

References · 53

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,950
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,318
  3. 2017Graph Attention Networkscited by 8,888
  4. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,379
  5. 2017Inductive Representation Learning on Large Graphscited by 6,303
  6. 2018Neural Ordinary Differential Equationscited by 3,750
  7. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,911
  8. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,157
  9. 2018Pitfalls of Graph Neural Network Evaluationcited by 1,003
  10. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 973
  11. 2019Hamiltonian Neural Networkscited by 705
  12. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 396
38 more
  1. 2018Deep Learning on Graphs: A Surveycited by 393
  2. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 371
  3. 2017Stable Architectures for Deep Neural Networkscited by 340
  4. 2019Adversarial Attacks on Graph Neural Networks via Meta Learningcited by 261
  5. 2021GRAND: Graph Neural Diffusioncited by 258
  6. 2020Graph Random Neural Network for Semi-Supervised Learning on Graphscited by 213
  7. 2020Data Augmentation for Graph Neural Networkscited by 203
  8. 2020GNNGuard: Defending Graph Neural Networks against Adversarial Attackscited by 195
  9. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  10. 2019Symplectic Recurrent Neural Networkscited by 149
  11. 2021Sinkformers: Transformers with Doubly Stochastic Attentioncited by 137
  12. 2022Graph-Coupled Oscillator Networkscited by 124
  13. 2017Topology Adaptive Graph Convolutional Networkscited by 112
  14. 2021Robustness of Graph Neural Networks at Scalecited by 100
  15. 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
  16. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  17. 2019On Robustness of Neural Ordinary Differential Equationscited by 83
  18. 2020DeepRobust: A PyTorch Library for Adversarial Attacks and Defensescited by 78
  19. 2016Hiding Individuals and Communities in a Social Networkcited by 77
  20. 2021TDGIA:Effective Injection Attacks on Graph Neural Networkscited by 67
  21. 2018Fast Gradient Attack on Network Embeddingcited by 65
  22. 2022Understanding and Improving Graph Injection Attack by Promoting Unnoticeabilitycited by 62
  23. 2019Graph Embedding on Biomedical Networks: Methods, Applications, and Evaluationscited by 50
  24. 2020Scalable Attack on Graph Data by Injecting Vicious Nodescited by 50
  25. 2021Graph Robustness Benchmark: Benchmarking the Adversarial Robustness of Graph Machine Learningcited by 44
  26. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  27. 2022Reliable Representations Make A Stronger Defender: Unsupervised Structure Refinement for Robust GNNcited by 34
  28. 2022On the Robustness of Graph Neural Diffusion to Topology Perturbationscited by 30
  29. 2023Graph Neural Convection-Diffusion with Heterophilycited by 26
  30. 2020Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradientscited by 22
  31. 2021Adversarial Attack on Graph Neural Networks as An Influence Maximization Problemcited by 20
  32. 2022RobustLoc: Robust Camera Pose Regression in Challenging Driving Environmentscited by 18
  33. 2022SGAT: Simplicial Graph Attention Networkcited by 16
  34. 2022GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networkscited by 14
  35. 2022Adversarial Inter-Group Link Injection Degrades the Fairness of Graph Neural Networkscited by 12
  36. 2022Spectral Adversarial Training for Robust Graph Neural Networkcited by 12
  37. 2023Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networkscited by 12
  38. 2023Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networkscited by 11

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 3; 2024: 12; 2025: 6; 2026: 3.

24 papers.

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  1. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  2. 2024Can Large Language Models Improve the Adversarial Robustness of Graph Neural Networks?cited by 22
  3. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  4. 2023Robust Graph Neural Networks via Unbiased Aggregationcited by 8
  5. 2024Distributed-Order Fractional Graph Operating Networkcited by 7
  6. 2024PointDifformer: Robust Point Cloud Registration With Neural Diffusion and Transformercited by 6
  7. 2024SAGMAN: Stability Analysis of Graph Neural Networks on the Manifoldscited by 4
  8. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  9. 2024Enhancing the Resilience of Graph Neural Networks to Topological Perturbations in Sparse Graphscited by 3
  10. 2024Bridging Large Language Models and Graph Structure Learning Models for Robust Representation Learningcited by 3
  11. 2024PosDiffNet: Positional Neural Diffusion for Point Cloud Registration in a Large Field of View with Perturbationscited by 2
  12. 2024PRFusion: Toward Effective and Robust Multi-Modal Place Recognition with Image and Point Cloud Fusioncited by 2
12 more
  1. 2023Resilient Graph Neural Networks: A Coupled Dynamical Systems Approachcited by 1
  2. 2025Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibriumcited by 1
  3. 2025A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Datacited by 1
  4. 2024Adversarial Robustness of Link Sign Prediction in Signed Graphscited by 0
  5. 2024Graph Adversarial Diffusion Convolutioncited by 0
  6. 2024Information propagation dynamics in Deep Graph Networkscited by 0
  7. 2025Improving Adversarial Robustness via Phase and Amplitude-aware Promptingcited by 0
  8. 2025JANUS: A Dual-Constraint Generative Framework for Stealthy Node Injection Attackscited by 0
  9. 2025Learning Aligned Stability in Neural ODEs Reconciling Accuracy with Robustnesscited by 0
  10. 2026Lyapunov Stable Graph Neural Flowcited by 0
  11. 2026TopFeaRe: Locating Critical State of Adversarial Resilience for Graphs Regarding Topology-Feature Entanglementcited by 0
  12. 2026Let Prompts Bridge Defense Knowledge: Transferable Graph Purification via Vulnerability-Aware GPLcited by 0