mlsanityData to 7 Oct 2026

On the Robustness of Graph Neural Diffusion to Topology Perturbations

arXiv 2209.07754 ↗First posted 16 Sep 2022cs.LGcited by 30

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Abstract (arXiv)

Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural PDE framework based on which a new class of robust GNNs can be defined. We verify that the new model achieves comparable state-of-the-art performance on several benchmark datasets.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 33 of its 60 references that are in the map. First posted on arXiv 16 Sep 2022.

Builds on

33 of 60 references.

References · 33

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  7. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  8. 2016Variational Graph Auto-Encoderscited by 1,373
  9. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,133
  10. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  11. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  12. 2015Image-based Recommendations on Styles and Substitutescited by 702
21 more
  1. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  2. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 395
  3. 2018Deep Learning on Graphs: A Surveycited by 393
  4. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 368
  5. 2017Stable Architectures for Deep Neural Networkscited by 340
  6. 2019Adversarial Attacks on Graph Neural Networks via Meta Learningcited by 261
  7. 2021GRAND: Graph Neural Diffusioncited by 258
  8. 2020Graph Random Neural Network for Semi-Supervised Learning on Graphscited by 213
  9. 2020GNNGuard: Defending Graph Neural Networks against Adversarial Attackscited by 195
  10. 2017Topology Adaptive Graph Convolutional Networkscited by 112
  11. 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
  12. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  13. 2019On Robustness of Neural Ordinary Differential Equationscited by 83
  14. 2016Hiding Individuals and Communities in a Social Networkcited by 77
  15. 2021TDGIA:Effective Injection Attacks on Graph Neural Networkscited by 67
  16. 2018Fast Gradient Attack on Network Embeddingcited by 65
  17. 2020Graph Geometry Interaction Learningcited by 55
  18. 2019Graph Embedding on Biomedical Networks: Methods, Applications, and Evaluationscited by 50
  19. 2020Scalable Attack on Graph Data by Injecting Vicious Nodescited by 50
  20. 2021Graph Robustness Benchmark: Benchmarking the Adversarial Robustness of Graph Machine Learningcited by 44
  21. 2021Lipschitz Normalization for Self-Attention Layers with Application to Graph Neural Networkscited by 38

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 10; 2024: 10; 2025: 8; 2026: 1.

30 papers.

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  1. 2023Graph Neural Convection-Diffusion with Heterophilycited by 26
  2. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  3. 2023Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approachcited by 24
  4. 2022RobustLoc: Robust Camera Pose Regression in Challenging Driving Environmentscited by 18
  5. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  6. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  7. 2023A Generalized Neural Diffusion Framework on Graphscited by 13
  8. 2023Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networkscited by 12
  9. 2023Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networkscited by 11
  10. 2024Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Studycited by 9
  11. 2024Understanding Oversmoothing in Diffusion-Based GNNs From the Perspective of Operator Semigroup Theorycited by 8
  12. 2024Continuous Product Graph Neural Networkscited by 8
18 more
  1. 2024Distributed-Order Fractional Graph Operating Networkcited by 7
  2. 2024PointDifformer: Robust Point Cloud Registration With Neural Diffusion and Transformercited by 6
  3. 2023RobustMat: Neural Diffusion for Street Landmark Patch Matching under Challenging Environmentscited by 5
  4. 2025Neural Variable-Order Fractional Differential Equation Networkscited by 5
  5. 2024SAGMAN: Stability Analysis of Graph Neural Networks on the Manifoldscited by 4
  6. 2024PosDiffNet: Positional Neural Diffusion for Point Cloud Registration in a Large Field of View with Perturbationscited by 2
  7. 2024Continuous Geometry-Aware Graph Diffusion via Hyperbolic Neural PDEcited by 2
  8. 2024PRFusion: Toward Effective and Robust Multi-Modal Place Recognition with Image and Point Cloud Fusioncited by 2
  9. 2025Continuous Simplicial Neural Networkscited by 2
  10. 2025GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learningcited by 2
  11. 2023Resilient Graph Neural Networks: A Coupled Dynamical Systems Approachcited by 1
  12. 2025Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibriumcited by 1
  13. 2023Node Embedding from Hamiltonian Information Propagation in Graph Neural Networkscited by 0
  14. 2023Generalized Graphon Process: Convergence of Graph Frequencies in Stretched Cut Distancecited by 0
  15. 2025Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  16. 2025Second-Order Tensorial Partial Differential Equations on Graphscited by 0
  17. 2025Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  18. 2026Lyapunov Stable Graph Neural Flowcited by 0