mlsanityData to 14 Oct 2026

Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature

arXiv 2211.15779 ↗First posted 28 Nov 2022cs.LG stat.MLcited by 98

Not on the map. Why?

Abstract (arXiv)

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking into account distant information. Our study reveals the key connection between the local graph geometry and the occurrence of both of these issues, thereby providing a unified framework for studying them at a local scale using the Ollivier-Ricci curvature. Specifically, we demonstrate that over-smoothing is linked to positive graph curvature while over-squashing is linked to negative graph curvature. Based on our theory, we propose the Batch Ollivier-Ricci Flow, a novel rewiring algorithm capable of simultaneously addressing both over-smoothing and over-squashing.

Key facts. Cited by 98 papers in the map (data through 14 Oct 2026). Builds on 46 of its 85 references that are in the map. First posted on arXiv 28 Nov 2022.

Builds on

46 of 85 references.

References · 46

  1. 2017Attention Is All You Needcited by 60,361
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  4. 2017Graph Attention Networkscited by 8,923
  5. 2017Inductive Representation Learning on Large Graphscited by 6,320
  6. 2018How Powerful are Graph Neural Networks?cited by 4,393
  7. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  8. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,434
  9. 2017Modeling Relational Data with Graph Convolutional Networkscited by 1,694
  10. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  11. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,138
  12. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
34 more
  1. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 976
  2. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 877
  3. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  4. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 754
  5. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 728
  6. 2019Graph Neural Networks for Social Recommendationcited by 714
  7. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 680
  8. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  9. 2019Multi-scale Attributed Node Embeddingcited by 548
  10. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
  11. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 478
  12. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 415
  13. 2019Diffusion Improves Graph Learningcited by 414
  14. 2018Neural Relational Inference for Interacting Systemscited by 339
  15. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 305
  16. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  17. 2022Long Range Graph Benchmarkcited by 263
  18. 2020A Note on Over-Smoothing for Graph Neural Networkscited by 249
  19. 2018Graph networks as learnable physics engines for inference and controlcited by 244
  20. 2018Learning Deep Generative Models of Graphscited by 229
  21. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  22. 2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
  23. 2018End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completioncited by 136
  24. 2018NetGAN: Generating Graphs via Random Walkscited by 131
  25. 2022Graph-Coupled Oscillator Networkscited by 124
  26. 2022FoSR: First-order spectral rewiring for addressing oversquashing in GNNscited by 105
  27. 2019Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networkscited by 62
  28. 2022Oversquashing in GNNs through the lens of information contraction and graph expansioncited by 53
  29. 2019Dual Graph Attention Networks for Deep Latent Representation of Multifaceted Social Effects in Recommender Systemscited by 41
  30. 2021Conditional Neural Relational Inference for Interacting Systemscited by 28
  31. 2019Exploring Graph Neural Networks for Stock Market Predictions with Rolling Window Analysiscited by 27
  32. 2015Ricci Curvature of the Internet Topologycited by 22
  33. 2022Rewiring Networks for Graph Neural Network Training Using Discrete Geometrycited by 14
  34. 2020Ollivier-Ricci curvature convergence in random geometric graphscited by 11

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 10; 2024: 28; 2025: 34; 2026: 26.

98 papers.

Sort:

By area:

  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  2. 2023Locality-Aware Graph-Rewiring in GNNscited by 56
  3. 2023Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvaturecited by 41
  4. 2023Graph Positional and Structural Encodercited by 33
  5. 2024How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashingcited by 24
  6. 2023Over-Squashing in Graph Neural Networks: A Comprehensive surveycited by 23
  7. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  8. 2024Cayley Graph Propagationcited by 21
  9. 2025Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learningcited by 19
  10. 2023Simplicial Representation Learning with Neural k-Formscited by 18
  11. 2023Effective Structural Encodings via Local Curvature Profilescited by 13
  12. 2024What Can We Learn from State Space Models for Machine Learning on Graphs?cited by 13
38 more
  1. 2024Revisiting Random Walks for Learning on Graphscited by 13
  2. 2025GNNs Getting ComFy: Community and Feature Similarity Guided Rewiringcited by 13
  3. 2024Joint Graph Rewiring and Feature Denoising via Spectral Resonancecited by 12
  4. 2025Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Taskscited by 12
  5. 2024The Effectiveness of Curvature-Based Rewiring and the Role of Hyperparameters in GNNs Revisitedcited by 11
  6. 2024PANDA: Expanded Width-Aware Message Passing Beyond Rewiringcited by 10
  7. 2024Graph Pooling via Ricci Flowcited by 10
  8. 2024UniIF: Unified Molecule Inverse Foldingcited by 9
  9. 2024Unitary convolutions for learning on graphs and groupscited by 8
  10. 2024Graph Rewiring in GNNs to Mitigate Over-Squashing and Over-Smoothing: A Surveycited by 8
  11. 2025Mitigating Over-Squashing in Graph Neural Networks by Spectrum-Preserving Sparsificationcited by 8
  12. 2024A Survey on Structure-Preserving Graph Transformerscited by 7
  13. 2025Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Modelscited by 7
  14. 2023From Cluster Assumption to Graph Convolution: Graph-based Semi-Supervised Learning Revisitedcited by 6
  15. 2024Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graphcited by 6
  16. 2025Are We Measuring Oversmoothing in Graph Neural Networks Correctly?cited by 6
  17. 2025PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networkscited by 6
  18. 2025DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomoleculescited by 5
  19. 2024IntraMix: Intra-Class Mixup Generation for Accurate Labels and Neighborscited by 4
  20. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  21. 2024Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networkscited by 4
  22. 2024Discrete Curvature Graph Information Bottleneckcited by 4
  23. 2025ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Spacecited by 4
  24. 2024Subhomogeneous Deep Equilibrium Modelscited by 3
  25. 2024Foundations and Frontiers of Graph Learning Theorycited by 3
  26. 2025Transformer Meets Twicing: Harnessing Unattended Residual Informationcited by 3
  27. 2025Influence Functions for Edge Edits in Non-Convex Graph Neural Networkscited by 3
  28. 2025Stuart-Landau Oscillatory Graph Neural Networkcited by 3
  29. 2026Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approachcited by 3
  30. 2024Differentiable Cluster Graph Neural Networkcited by 2
  31. 2024Scalable Graph Compressed Convolutionscited by 2
  32. 2024DuoGNN: Topology-aware Graph Neural Network with Homophily and Heterophily Interaction-Decouplingcited by 2
  33. 2024TANGNN: a Concise, Scalable and Effective Graph Neural Networks with Top-m Attention Mechanism for Graph Representation Learningcited by 2
  34. 2024Graph Neural Networks Need Cluster-Normalize-Activate Modulescited by 2
  35. 2025Performance Heterogeneity in Graph Neural Networks: Lessons for Architecture Design and Preprocessingcited by 2
  36. 2025Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passingcited by 2
  37. 2025Efficient Curvature-aware Graph Networkcited by 2
  38. 2026Position: Don't be Afraid of Over-Smoothing And Over-Squashingcited by 2

50 most cited of 98 All 98 (JSON)