mlsanityData to 7 Oct 2026

Orthogonal Graph Neural Networks

arXiv 2109.11338 ↗First posted 23 Sep 2021cs.LG cs.AIcited by 19

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Abstract (arXiv)

Graph neural networks (GNNs) have received tremendous attention due to their superiority in learning node representations. These models rely on message passing and feature transformation functions to encode the structural and feature information from neighbors. However, stacking more convolutional layers significantly decreases the performance of GNNs. Most recent studies attribute this limitation to the over-smoothing issue, where node embeddings converge to indistinguishable vectors. Through a number of experimental observations, we argue that the main factor degrading the performance is the unstable forward normalization and backward gradient resulted from the improper design of the feature transformation, especially for shallow GNNs where the over-smoothing has not happened. Therefore, we propose a novel orthogonal feature transformation, named Ortho-GConv, which could generally augment the existing GNN backbones to stabilize the model training and improve the model's generalization performance. Specifically, we maintain the orthogonality of the feature transformation comprehensively from three perspectives, namely hybrid weight initialization, orthogonal transformation, and orthogonal regularization. By equipping the existing GNNs (e.g. GCN, JKNet, GCNII) with Ortho-GConv, we demonstrate the generality of the orthogonal feature transformation to enable stable training, and show its effectiveness for node and graph classification tasks.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 43 of its 57 references that are in the map. First posted on arXiv 23 Sep 2021.

Builds on

43 of 57 references.

References · 43

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  4. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  5. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  7. 2019Simplifying Graph Convolutional Networkscited by 1,470
  8. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  9. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  10. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  11. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  12. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
31 more
  1. 2020Simple and Deep Graph Convolutional Networkscited by 857
  2. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  3. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
  4. 2013Exact solutions to the nonlinear dynamics of learning in deep linear neural networkscited by 748
  5. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  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. 2019Graph U-Netscited by 489
  9. 2016Learning Convolutional Neural Networks for Graphscited by 314
  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. 2015Deep Convolutional Networks on Graph-Structured Datacited by 246
  14. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  15. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
  16. 2018Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networkscited by 176
  17. 2018Adaptive Graph Convolutional Neural Networkscited by 155
  18. 2015A Simple Way to Initialize Recurrent Networks of Rectified Linear Unitscited by 130
  19. 2019Orthogonal Convolutional Neural Networkscited by 122
  20. 2020Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approachcited by 119
  21. 2020Towards Deeper Graph Neural Networks with Differentiable Group Normalizationcited by 113
  22. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  23. 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
  24. 2017Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networkscited by 92
  25. 2017On orthogonality and learning recurrent networks with long term dependenciescited by 82
  26. 2019Auto-GNN: Neural Architecture Search of Graph Neural Networkscited by 73
  27. 2018Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?cited by 62
  28. 2017All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulationcited by 58
  29. 2020ASGN: An Active Semi-supervised Graph Neural Network for Molecular Property Predictioncited by 58
  30. 2020Controllable Orthogonalization in Training DNNscited by 30
  31. 2021Adaptive Label Smoothing To Regularize Large-Scale Graph Trainingcited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 5; 2024: 11; 2025: 0; 2026: 2.

19 papers.

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  1. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 48
  2. 2024Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Modelscited by 21
  3. 2023Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networkscited by 18
  4. 2023Are GATs Out of Balance?cited by 9
  5. 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attackscited by 9
  6. 2024Unitary convolutions for learning on graphs and groupscited by 8
  7. 2024ADEdgeDrop: Adversarial Edge Dropping for Robust Graph Neural Networkscited by 7
  8. 2024Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterizationcited by 7
  9. 2024Efficient Sharpness-Aware Minimization for Molecular Graph Transformer Modelscited by 7
  10. 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equationcited by 6
  11. 2024Graph Unitary Message Passingcited by 5
  12. 2023Towards Better Graph Representation Learning with Parameterized Decomposition & Filteringcited by 4
7 more
  1. 2024Rethinking Independent Cross-Entropy Loss For Graph-Structured Datacited by 4
  2. 2023SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecastingcited by 1
  3. 2026DRGW: Learning Disentangled Representations for Robust Graph Watermarkingcited by 1
  4. 2022Mitigating Overfitting in Graph Neural Networks via Feature and Hyperplane Perturbationcited by 0
  5. 2023ID-MixGCL: Identity Mixup for Graph Contrastive Learningcited by 0
  6. 2024SES: Bridging the Gap Between Explainability and Prediction of Graph Neural Networkscited by 0
  7. 2026Exploring Oversmoothing with Householder Matricescited by 0