mlsanityData to 14 Oct 2026

Resilient Graph Neural Networks: A Coupled Dynamical Systems Approach

arXiv 2311.06942 ↗First posted 12 Nov 2023cs.LG cs.CRcited by 1

Not on the map. Why?

Abstract (arXiv)

Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to input perturbations in the form of adversarial attacks. This paper introduces an innovative approach to fortify GNNs against adversarial perturbations through the lens of coupled dynamical systems. Our method introduces graph neural layers based on differential equations with contractive properties, which, as we show, improve the robustness of GNNs. A distinctive feature of the proposed approach is the simultaneous learned evolution of both the node features and the adjacency matrix, yielding an intrinsic enhancement of model robustness to perturbations in the input features and the connectivity of the graph. We mathematically derive the underpinnings of our novel architecture and provide theoretical insights to reason about its expected behavior. We demonstrate the efficacy of our method through numerous real-world benchmarks, reading on par or improved performance compared to existing methods.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 45 of its 71 references that are in the map. First posted on arXiv 12 Nov 2023.

Builds on

45 of 71 references.

References · 45

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Graph Attention Networkscited by 8,923
  4. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  5. 2018Neural Ordinary Differential Equationscited by 3,779
  6. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
  7. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  8. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  9. 2019Diffusion Improves Graph Learningcited by 414
  10. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 397
  11. 2022Message Passing Neural PDE Solverscited by 386
  12. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 371
33 more
  1. 2018Invariant and Equivariant Graph Networkscited by 346
  2. 2017Stable Architectures for Deep Neural Networkscited by 341
  3. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 313
  4. 2019Adversarial Attacks on Graph Neural Networks via Meta Learningcited by 261
  5. 2021GRAND: Graph Neural Diffusioncited by 258
  6. 2020A Note on Over-Smoothing for Graph Neural Networkscited by 249
  7. 2020Graph Random Neural Network for Semi-Supervised Learning on Graphscited by 213
  8. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 195
  9. 2020GNNGuard: Defending Graph Neural Networks against Adversarial Attackscited by 195
  10. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  11. 2022Graph-Coupled Oscillator Networkscited by 124
  12. 2018Adversarial Attacks on Node Embeddings via Graph Poisoningcited by 109
  13. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  14. 2021Robustness of Graph Neural Networks at Scalecited by 100
  15. 2020Training robust neural networks using Lipschitz boundscited by 99
  16. 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
  17. 2016Hiding Individuals and Communities in a Social Networkcited by 77
  18. 2022Understanding and Improving Graph Injection Attack by Promoting Unnoticeabilitycited by 62
  19. 2022Understanding convolution on graphs via energiescited by 59
  20. 2018Limitations of the Lipschitz constant as a defense against adversarial examplescited by 49
  21. 2021Graph Robustness Benchmark: Benchmarking the Adversarial Robustness of Graph Machine Learningcited by 44
  22. 2023Are Defenses for Graph Neural Networks Robust?cited by 38
  23. 2022On the Robustness of Graph Neural Diffusion to Topology Perturbationscited by 30
  24. 2023Graph Neural Convection-Diffusion with Heterophilycited by 26
  25. 2023Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approachcited by 24
  26. 2023Robust Mid-Pass Filtering Graph Convolutional Networkscited by 17
  27. 2021Convolutional Normalization: Improving Deep Convolutional Network Robustness and Trainingcited by 15
  28. 2023Feature Transportation Improves Graph Neural Networkscited by 15
  29. 2022GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networkscited by 14
  30. 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
  31. 2022Dynamical systems' based neural networkscited by 10
  32. 2023Designing Stable Neural Networks using Convex Analysis and ODEscited by 10
  33. 2021Non-Euclidean Contraction Analysis of Continuous-Time Neural Networkscited by 2

Built on by

Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025Approximation theory for 1-Lipschitz ResNetscited by 7