Orthogonal Graph Neural Networks
Not on the map. Why?
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
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2017Graph Attention Networkscited by 8,854
- 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
- 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
- 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
- 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
- 2019Simplifying Graph Convolutional Networkscited by 1,470
- 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
- 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
- 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
- 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
- 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
31 more
- 2020Simple and Deep Graph Convolutional Networkscited by 857
- 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
- 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
- 2013Exact solutions to the nonlinear dynamics of learning in deep linear neural networkscited by 748
- 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
- 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
- 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
- 2019Graph U-Netscited by 489
- 2016Learning Convolutional Neural Networks for Graphscited by 314
- 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
- 2020Towards Deeper Graph Neural Networkscited by 296
- 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
- 2015Deep Convolutional Networks on Graph-Structured Datacited by 246
- 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
- 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
- 2018Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networkscited by 176
- 2018Adaptive Graph Convolutional Neural Networkscited by 155
- 2015A Simple Way to Initialize Recurrent Networks of Rectified Linear Unitscited by 130
- 2019Orthogonal Convolutional Neural Networkscited by 122
- 2020Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approachcited by 119
- 2020Towards Deeper Graph Neural Networks with Differentiable Group Normalizationcited by 113
- 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
- 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
- 2017Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networkscited by 92
- 2017On orthogonality and learning recurrent networks with long term dependenciescited by 82
- 2019Auto-GNN: Neural Architecture Search of Graph Neural Networkscited by 73
- 2018Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?cited by 62
- 2017All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulationcited by 58
- 2020ASGN: An Active Semi-supervised Graph Neural Network for Molecular Property Predictioncited by 58
- 2020Controllable Orthogonalization in Training DNNscited by 30
- 2021Adaptive Label Smoothing To Regularize Large-Scale Graph Trainingcited by 12
Built on by
Citing papers per year: 2022: 1; 2023: 5; 2024: 11; 2025: 0; 2026: 2.
19 papers.
Sort:
By area:
- 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 48
- 2024Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Modelscited by 21
- 2023Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networkscited by 18
- 2023Are GATs Out of Balance?cited by 9
- 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attackscited by 9
- 2024Unitary convolutions for learning on graphs and groupscited by 8
- 2024ADEdgeDrop: Adversarial Edge Dropping for Robust Graph Neural Networkscited by 7
- 2024Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterizationcited by 7
- 2024Efficient Sharpness-Aware Minimization for Molecular Graph Transformer Modelscited by 7
- 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equationcited by 6
- 2024Graph Unitary Message Passingcited by 5
- 2023Towards Better Graph Representation Learning with Parameterized Decomposition & Filteringcited by 4
7 more
- 2024Rethinking Independent Cross-Entropy Loss For Graph-Structured Datacited by 4
- 2023SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecastingcited by 1
- 2026DRGW: Learning Disentangled Representations for Robust Graph Watermarkingcited by 1
- 2022Mitigating Overfitting in Graph Neural Networks via Feature and Hyperplane Perturbationcited by 0
- 2023ID-MixGCL: Identity Mixup for Graph Contrastive Learningcited by 0
- 2024SES: Bridging the Gap Between Explainability and Prediction of Graph Neural Networkscited by 0
- 2026Exploring Oversmoothing with Householder Matricescited by 0
- 2026Exploring Oversmoothing with Householder Matrices12 Aug 2026
- 2026DRGW: Learning Disentangled Representations for Robust Graph Watermarking20 Jan 2026
- 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equation15 Nov 2024
- 2024Unitary convolutions for learning on graphs and groups7 Oct 2024
- 2024SES: Bridging the Gap Between Explainability and Prediction of Graph Neural Networks16 Jul 2024
- 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning26 Jun 2024
- 2024Efficient Sharpness-Aware Minimization for Molecular Graph Transformer Models19 Jun 2024
- 2024Rethinking Independent Cross-Entropy Loss For Graph-Structured Data24 May 2024
- 2024Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterization14 May 2024
- 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attacks27 Apr 2024
- 2024Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models24 Apr 2024
- 2024Graph Unitary Message Passing17 Mar 2024
7 more
- 2024ADEdgeDrop: Adversarial Edge Dropping for Robust Graph Neural Networks14 Mar 2024
- 2023SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecasting5 Dec 2023
- 2023Are GATs Out of Balance?11 Oct 2023
- 2023Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks31 Aug 2023
- 2023Towards Better Graph Representation Learning with Parameterized Decomposition & Filtering10 May 2023
- 2023ID-MixGCL: Identity Mixup for Graph Contrastive Learning20 Apr 2023
- 2022Mitigating Overfitting in Graph Neural Networks via Feature and Hyperplane Perturbation28 Nov 2022
- 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 48
- 2023Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networkscited by 18
- 2023Are GATs Out of Balance?cited by 9
- 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attackscited by 9
- 2024Unitary convolutions for learning on graphs and groupscited by 8
- 2024ADEdgeDrop: Adversarial Edge Dropping for Robust Graph Neural Networkscited by 7
- 2024Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterizationcited by 7
- 2024Efficient Sharpness-Aware Minimization for Molecular Graph Transformer Modelscited by 7
- 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equationcited by 6
- 2024Graph Unitary Message Passingcited by 5
- 2023Towards Better Graph Representation Learning with Parameterized Decomposition & Filteringcited by 4
- 2024Rethinking Independent Cross-Entropy Loss For Graph-Structured Datacited by 4
12 most cited of 18 All 18 (JSON)
- 2026Exploring Oversmoothing with Householder Matrices12 Aug 2026
- 2026DRGW: Learning Disentangled Representations for Robust Graph Watermarking20 Jan 2026
- 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equation15 Nov 2024
- 2024Unitary convolutions for learning on graphs and groups7 Oct 2024
- 2024SES: Bridging the Gap Between Explainability and Prediction of Graph Neural Networks16 Jul 2024
- 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning26 Jun 2024
- 2024Efficient Sharpness-Aware Minimization for Molecular Graph Transformer Models19 Jun 2024
- 2024Rethinking Independent Cross-Entropy Loss For Graph-Structured Data24 May 2024
- 2024Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterization14 May 2024
- 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attacks27 Apr 2024
- 2024Graph Unitary Message Passing17 Mar 2024
- 2024ADEdgeDrop: Adversarial Edge Dropping for Robust Graph Neural Networks14 Mar 2024
12 newest of 18 All 18 (JSON)