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A Survey on Oversmoothing in Graph Neural Networks

arXiv 2303.10993 ↗First posted 20 Mar 2023cs.LGcited by 246

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Abstract (arXiv)

Node features of graph neural networks (GNNs) tend to become more similar with the increase of the network depth. This effect is known as over-smoothing, which we axiomatically define as the exponential convergence of suitable similarity measures on the node features. Our definition unifies previous approaches and gives rise to new quantitative measures of over-smoothing. Moreover, we empirically demonstrate this behavior for several over-smoothing measures on different graphs (small-, medium-, and large-scale). We also review several approaches for mitigating over-smoothing and empirically test their effectiveness on real-world graph datasets. Through illustrative examples, we demonstrate that mitigating over-smoothing is a necessary but not sufficient condition for building deep GNNs that are expressive on a wide range of graph learning tasks. Finally, we extend our definition of over-smoothing to the rapidly emerging field of continuous-time GNNs.

Key facts. Cited by 246 papers in the map (data through 7 Oct 2026). Builds on 39 of its 53 references that are in the map. First posted on arXiv 20 Mar 2023.

Builds on

39 of 53 references.

References · 39

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2017Inductive Representation Learning on Large Graphscited by 6,284
  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  7. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  8. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  9. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,133
  10. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  11. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  12. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
27 more
  1. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  2. 2020Simple and Deep Graph Convolutional Networkscited by 857
  3. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  4. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  5. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 624
  6. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  7. 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
  8. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  9. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  10. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  11. 2020Towards Deeper Graph Neural Networkscited by 296
  12. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  13. 2021GRAND: Graph Neural Diffusioncited by 258
  14. 2020A Note on Over-Smoothing for Graph Neural Networkscited by 245
  15. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  16. 2019Graph Neural Ordinary Differential Equationscited by 153
  17. 2022Graph-Coupled Oscillator Networkscited by 123
  18. 2019Continuous Graph Neural Networkscited by 114
  19. 2020Towards Deeper Graph Neural Networks with Differentiable Group Normalizationcited by 113
  20. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  21. 2022Not too little, not too much: a theoretical analysis of graph (over)smoothingcited by 106
  22. 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
  23. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  24. 2020Bayesian Graph Neural Networks with Adaptive Connection Samplingcited by 81
  25. 2022Expander Graph Propagationcited by 75
  26. 2020Understanding and Resolving Performance Degradation in Graph Convolutional Networkscited by 53
  27. 2022Gradient Gating for Deep Multi-Rate Learning on Graphscited by 49

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 32; 2024: 89; 2025: 73; 2026: 52.

246 papers.

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  1. 2023Large Language Models on Graphs: A Comprehensive Surveycited by 190
  2. 2024Graph Mamba: Towards Learning on Graphs with State Space Modelscited by 84
  3. 2024CARTE: Pretraining and Transfer for Tabular Learningcited by 69
  4. 2023How does over-squashing affect the power of GNNs?cited by 53
  5. 2023Demystifying Oversmoothing in Attention-Based Graph Neural Networkscited by 47
  6. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  7. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 42
  8. 2023Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?cited by 41
  9. 2024Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNscited by 31
  10. 2024Kolmogorov-Arnold Graph Neural Networkscited by 31
  11. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  12. 2023Graph Deep Learning for Time Series Forecastingcited by 26
38 more
  1. 2024How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashingcited by 24
  2. 2024Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulationscited by 24
  3. 2023Over-Squashing in Graph Neural Networks: A Comprehensive surveycited by 23
  4. 2023Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreachingcited by 23
  5. 2024Spectral Graph Pruning Against Over-Squashing and Over-Smoothingcited by 23
  6. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  7. 2024Cayley Graph Propagationcited by 21
  8. 2023Permutation Equivariant Graph Framelets for Heterophilous Graph Learningcited by 19
  9. 2023Graph Meets LLMs: Towards Large Graph Modelscited by 19
  10. 2024Setting the Record Straight on Transformer Oversmoothingcited by 19
  11. 2023Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networkscited by 18
  12. 2025Towards Quantifying Long-Range Interactions in Graph Machine Learning: a Large Graph Dataset and a Measurementcited by 18
  13. 2025Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learningcited by 18
  14. 2023Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networkscited by 17
  15. 2023Segment Anything in Non-Euclidean Domains: Challenges and Opportunitiescited by 16
  16. 2023Neural Oscillators are Universalcited by 16
  17. 2023Graph-based Time Series Clustering for End-to-End Hierarchical Forecastingcited by 16
  18. 2024Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patchingcited by 16
  19. 2023GraphGPT: Generative Pre-trained Graph Eulerian Transformercited by 15
  20. 2024Graph-based Forecasting with Missing Data through Spatiotemporal Downsamplingcited by 15
  21. 2024"Where am I?" Scene Retrieval with Languagecited by 15
  22. 2024VN-EGNN: E(3)-Equivariant Graph Neural Networks with Virtual Nodes Enhance Protein Binding Site Identificationcited by 14
  23. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  24. 2025Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approachcited by 14
  25. 2024A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directionscited by 13
  26. 2024Towards Neural Scaling Laws on Graphscited by 13
  27. 2024What Can We Learn from State Space Models for Machine Learning on Graphs?cited by 13
  28. 2024Even Sparser Graph Transformerscited by 12
  29. 2025DeepGate4: Efficient and Effective Representation Learning for Circuit Design at Scalecited by 12
  30. 2023Graph Convolutions Enrich the Self-Attention in Transformers!cited by 11
  31. 2024Non-convolutional Graph Neural Networkscited by 11
  32. 2025Generative Graph Pattern Machinecited by 11
  33. 2023A Metadata-Driven Approach to Understand Graph Neural Networkscited by 10
  34. 2024Mitigating Oversmoothing Through Reverse Process of GNNs for Heterophilic Graphscited by 10
  35. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
  36. 2024On The Temporal Domain of Differential Equation Inspired Graph Neural Networkscited by 9
  37. 2024A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspectivecited by 9
  38. 2024Continuous Product Graph Neural Networkscited by 8

50 most cited of 246 All 246 (JSON)