mlsanityData to 7 Oct 2026

Dissecting the Diffusion Process in Linear Graph Convolutional Networks

arXiv 2102.10739 ↗First posted 22 Feb 2021cs.LGcited by 58

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Abstract (arXiv)

Graph Convolutional Networks (GCNs) have attracted more and more attentions in recent years. A typical GCN layer consists of a linear feature propagation step and a nonlinear transformation step. Recent works show that a linear GCN can achieve comparable performance to the original non-linear GCN while being much more computationally efficient. In this paper, we dissect the feature propagation steps of linear GCNs from a perspective of continuous graph diffusion, and analyze why linear GCNs fail to benefit from more propagation steps. Following that, we propose Decoupled Graph Convolution (DGC) that decouples the terminal time and the feature propagation steps, making it more flexible and capable of exploiting a very large number of feature propagation steps. Experiments demonstrate that our proposed DGC improves linear GCNs by a large margin and makes them competitive with many modern variants of non-linear GCNs.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). Builds on 29 of its 36 references that are in the map. First posted on arXiv 22 Feb 2021.

Builds on

29 of 36 references.

References · 29

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  4. 2017Graph Attention Networkscited by 8,854
  5. 2017Inductive Representation Learning on Large Graphscited by 6,284
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  8. 2014DeepWalk: Online Learning of Social Representationscited by 1,543
  9. 2019Simplifying Graph Convolutional Networkscited by 1,470
  10. 2018Deep Graph Infomaxcited by 1,101
  11. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  12. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
17 more
  1. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  2. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  3. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  4. 2019GraphSAINT: Graph Sampling Based Inductive Learning Methodcited by 618
  5. 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 583
  6. 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
  7. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  8. 2020SIGN: Scalable Inception Graph Neural Networkscited by 283
  9. 2017Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equationscited by 203
  10. 2020Graph-Bert: Only Attention is Needed for Learning Graph Representationscited by 176
  11. 2019Graph Neural Ordinary Differential Equationscited by 153
  12. 2019Graph Wavelet Neural Networkcited by 131
  13. 2019Continuous Graph Neural Networkscited by 114
  14. 2019Certifiable Robustness to Graph Perturbationscited by 62
  15. 2020Graph Convolutional Networks using Heat Kernel for Semi-supervised Learningcited by 50
  16. 2019GResNet: Graph Residual Network for Reviving Deep GNNs from Suspended Animationcited by 21
  17. 2013The nonlinear heat equation on dense graphs and graph limitscited by 9

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Cited by year

Citing papers per year: 2021: 4; 2022: 9; 2023: 14; 2024: 17; 2025: 14.

58 papers.

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  1. 2023DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusioncited by 85
  2. 2022Multivariate Time Series Forecasting with Dynamic Graph Neural ODEscited by 72
  3. 2022Anti-Symmetric DGN: a stable architecture for Deep Graph Networkscited by 58
  4. 2021Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoodscited by 57
  5. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  6. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 42
  7. 2023Towards Understanding the Generalization of Graph Neural Networkscited by 41
  8. 2022Blurring-Sharpening Process Models for Collaborative Filteringcited by 35
  9. 2022Optimization-Induced Graph Implicit Nonlinear Diffusioncited by 28
  10. 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
  11. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  12. 2024Long Range Propagation on Continuous-Time Dynamic Graphscited by 26
38 more
  1. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  2. 2023Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreachingcited by 23
  3. 2022Geometric Knowledge Distillation: Topology Compression for Graph Neural Networkscited by 22
  4. 2023A Message Passing Perspective on Learning Dynamics of Contrastive Learningcited by 22
  5. 2023Laplacian Canonization: A Minimalist Approach to Sign and Basis Invariant Spectral Embeddingcited by 21
  6. 2021Climate Modeling with Neural Diffusion Equationscited by 20
  7. 2023Deep learning for dynamic graphs: models and benchmarkscited by 19
  8. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  9. 2024Rethinking Node-wise Propagation for Large-scale Graph Learningcited by 16
  10. 2024SA-GDA: Spectral Augmentation for Graph Domain Adaptationcited by 16
  11. 2022ResNorm: Tackling Long-tailed Degree Distribution Issue in Graph Neural Networks via Normalizationcited by 15
  12. 2023Reconstructing Graph Diffusion History from a Single Snapshotcited by 13
  13. 2023A Generalized Neural Diffusion Framework on Graphscited by 13
  14. 2025Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Taskscited by 12
  15. 2024Temporal Graph ODEs for Irregularly-Sampled Time Seriescited by 11
  16. 2021SkipNode: On Alleviating Performance Degradation for Deep Graph Convolutional Networkscited by 10
  17. 2022Less is More: SlimG for Accurate, Robust, and Interpretable Graph Miningcited by 10
  18. 2022Generalized energy and gradient flow via graph frameletscited by 10
  19. 2025Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modelingcited by 9
  20. 2024A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectivenesscited by 6
  21. 2024Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approachcited by 5
  22. 2023RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendationcited by 3
  23. 2024NetInfoF Framework: Measuring and Exploiting Network Usable Informationcited by 3
  24. 2023Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothingcited by 2
  25. 2024Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregationcited by 2
  26. 2024Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networkscited by 2
  27. 2024Graph Neural Aggregation-diffusion with Metastabilitycited by 2
  28. 2025A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNscited by 2
  29. 2025Graph Wave Networkscited by 2
  30. 2025Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equationscited by 2
  31. 2023Revisiting Generalized p-Laplacian Regularized Framelet GCNs: Convergence, Energy Dynamic and Training with Non-Linear Diffusioncited by 1
  32. 2024More Discriminative Sentence Embeddings via Semantic Graph Smoothingcited by 1
  33. 2025Resolving Oversmoothing with Opinion Dissensuscited by 1
  34. 2025Parameter-Free Hypergraph Neural Network for Few-Shot Node Classificationcited by 1
  35. 2025Gauge-Equivariant Graph Networks via Self-Interference Cancellationcited by 1
  36. 2025Measuring Over-smoothing beyond Dirichlet energycited by 1
  37. 2023Simple yet Effective Gradient-Free Graph Convolutional Networkscited by 0
  38. 2024Online Algorithm for Node Feature Forecasting in Temporal Graphscited by 0

50 most cited of 58 All 58 (JSON)