mlsanityData to 7 Oct 2026

A Note on Over-Smoothing for Graph Neural Networks

arXiv 2006.13318 ↗First posted 23 Jun 2020cs.LG stat.MLcited by 245

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Abstract (arXiv)

Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as over-smoothing, has been analyzed mostly in linear cases. In this paper, we build upon previous results citeoono2019graph to further analyze the over-smoothing effect in the general graph neural network architecture. We show when the weight matrix satisfies the conditions determined by the spectrum of augmented normalized Laplacian, the Dirichlet energy of embeddings will converge to zero, resulting in the loss of discriminative power. Using Dirichlet energy to measure "expressiveness" of embedding is conceptually clean; it leads to simpler proofs than citeoono2019graph and can handle more non-linearities.

Key facts. Cited by 245 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Jun 2020.

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Citing papers per year: 2021: 16; 2022: 36; 2023: 53; 2024: 59; 2025: 46; 2026: 35.

245 papers.

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  1. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
  2. 2023Language is All a Graph Needscited by 219
  3. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  4. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  5. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
  6. 2022Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practicecited by 136
  7. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  8. 2022FoSR: First-order spectral rewiring for addressing oversquashing in GNNscited by 104
  9. 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
  10. 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
  11. 2023Understanding Oversquashing in GNNs through the Lens of Effective Resistancecited by 94
  12. 2024Position: Graph Foundation Models are Already Herecited by 84
38 more
  1. 2023DRew: Dynamically Rewired Message Passing with Delaycited by 81
  2. 2023On the Connection Between MPNN and Graph Transformercited by 60
  3. 2021On Provable Benefits of Depth in Training Graph Convolutional Networkscited by 58
  4. 2022Understanding convolution on graphs via energiescited by 58
  5. 2023How does over-squashing affect the power of GNNs?cited by 53
  6. 2023Demystifying Oversmoothing in Attention-Based Graph Neural Networkscited by 47
  7. 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
  8. 2021Simple GNN Regularisation for 3D Molecular Property Prediction & Beyondcited by 44
  9. 2021AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filtercited by 43
  10. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 42
  11. 2022Simplicial Attention Networkscited by 40
  12. 2023Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvaturecited by 39
  13. 2021Transformers Generalize DeepSets and Can be Extended to Graphs and Hypergraphscited by 35
  14. 2023GraphControl: Adding Conditional Control to Universal Graph Pre-trained Models for Graph Domain Transfer Learningcited by 32
  15. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  16. 2024Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNscited by 31
  17. 2022Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Modelscited by 29
  18. 2026A Mechanistic Analysis of Looped Reasoning Language Modelscited by 27
  19. 2021Scalable deeper graph neural networks for high-performance materials property predictioncited by 26
  20. 2022Model Degradation Hinders Deep Graph Neural Networkscited by 26
  21. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  22. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  23. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 25
  24. 2025A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detectioncited by 24
  25. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  26. 2021Evaluating Deep Graph Neural Networkscited by 19
  27. 2022Preventing Over-Smoothing for Hypergraph Neural Networkscited by 19
  28. 2022Improving Graph Neural Networks with Learnable Propagation Operatorscited by 19
  29. 2023A Neural Collapse Perspective on Feature Evolution in Graph Neural Networkscited by 19
  30. 2023Deep learning for dynamic graphs: models and benchmarkscited by 19
  31. 2022Learning Spatial-Frequency Transformer for Visual Object Trackingcited by 18
  32. 2023Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networkscited by 18
  33. 2025Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learningcited by 18
  34. 2024Understanding and Mitigating Bottlenecks of State Space Models through the Lens of Recency and Over-smoothingcited by 17
  35. 2023Alleviating Over-smoothing for Unsupervised Sentence Representationcited by 16
  36. 2023Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecastingcited by 16
  37. 2023Dynamic Graph Representation Learning with Neural Networks: A Surveycited by 15
  38. 2023Feature Transportation Improves Graph Neural Networkscited by 15

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