Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networks
Not on the map. Why?
Abstract (arXiv)
Recently, neural network based approaches have achieved significant improvement for solving large, complex, graph-structured problems. However, their bottlenecks still need to be addressed, and the advantages of multi-scale information and deep architectures have not been sufficiently exploited. In this paper, we theoretically analyze how existing Graph Convolutional Networks (GCNs) have limited expressive power due to the constraint of the activation functions and their architectures. We generalize spectral graph convolution and deep GCN in block Krylov subspace forms and devise two architectures, both with the potential to be scaled deeper but each making use of the multi-scale information in different ways. We further show that the equivalence of these two architectures can be established under certain conditions. On several node classification tasks, with or without the help of validation, the two new architectures achieve better performance compared to many state-of-the-art methods.
Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jun 2019.
Builds on
No reference list yet.
Built on by
Citing papers per year: 2021: 16; 2022: 15; 2023: 15; 2024: 11; 2025: 4; 2026: 1.
62 papers.
Sort:
- 2023Language is All a Graph Needscited by 219
- 2022Revisiting Heterophily For Graph Neural Networkscited by 169
- 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
- 2022Decoupling the Depth and Scope of Graph Neural Networkscited by 94
- 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
- 2021Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoodscited by 57
- 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
- 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
- 2021Sampling methods for efficient training of graph convolutional networks: A surveycited by 40
- 2021Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Studycited by 36
- 2022Rewiring with Positional Encodings for Graph Neural Networkscited by 35
- 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
38 more
- 2021Scalable deeper graph neural networks for high-performance materials property predictioncited by 26
- 2022Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networkscited by 19
- 2022Affinity-Aware Graph Networkscited by 17
- 2021Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filteringcited by 14
- 2022Skeleton-based Action Recognition via Temporal-Channel Aggregationcited by 13
- 2022Learnable Filters for Geometric Scattering Modulescited by 9
- 2024What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networkscited by 9
- 2021MGC: A Complex-Valued Graph Convolutional Network for Directed Graphscited by 7
- 2023Neighborhood Homophily-based Graph Convolutional Networkcited by 7
- 2023When Do Graph Neural Networks Help with Node Classification? Investigating the Impact of Homophily Principle on Node Distinguishabilitycited by 7
- 2021Search For Deep Graph Neural Networkscited by 6
- 2022Graph Neural Networks Intersect Probabilistic Graphical Models: A Surveycited by 6
- 2024Representation Learning on Heterophilic Graph with Directional Neighborhood Attentioncited by 6
- 2023Clarify Confused Nodes via Separated Learningcited by 5
- 2024GCEPNet: Graph Convolution-Enhanced Expectation Propagation for Massive MIMO Detectioncited by 5
- 2021Spatio-Temporal Dual Graph Neural Networks for Travel Time Estimationcited by 4
- 2023Multitask Weakly Supervised Learning for Origin Destination Travel Time Estimationcited by 4
- 2021Multi-scale Graph Convolutional Networks with Self-Attentioncited by 3
- 2023Dirichlet Energy Enhancement of Graph Neural Networks by Framelet Augmentationcited by 3
- 2024Foundations and Frontiers of Graph Learning Theorycited by 3
- 2024Revealing the Pitfalls and Re-Evaluating the Advancement of Heterophilic Graph Learningcited by 3
- 2024Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learningcited by 3
- 2021Schema-Aware Deep Graph Convolutional Networks for Heterogeneous Graphscited by 2
- 2022LEReg: Empower Graph Neural Networks with Local Energy Regularizationcited by 2
- 2023Reducing Over-smoothing in Graph Neural Networks Using Relational Embeddingscited by 2
- 2024Structure-Aware Consensus Network on Graphs with Few Labeled Nodescited by 2
- 2021Dual GNNs: Graph Neural Network Learning with Limited Supervisioncited by 1
- 2021SoGCN: Second-Order Graph Convolutional Networkscited by 1
- 2022A Simple Way to Learn Metrics Between Attributed Graphscited by 1
- 2022GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomialscited by 1
- 2022When Do We Need Graph Neural Networks for Node Classification?cited by 1
- 2023Transformer and Snowball Graph Convolution Learning for Brain functional network Classificationcited by 1
- 2023Distributional Signals for Node Classification in Graph Neural Networkscited by 1
- 2023On Addressing the Limitations of Graph Neural Networkscited by 1
- 2023Theater Aid System for the Visually Impaired Through Transfer Learning of Spatio-Temporal Graph Convolution Networkscited by 1
- 2023Curriculum-Enhanced Residual Soft An-Isotropic Normalization for Over-smoothness in Deep GNNscited by 1
- 2024Graph Neural Networks for Parkinsons Disease Detectioncited by 1
- 2024Partially Trained Graph Convolutional Networks Resist Oversmoothingcited by 1
50 most cited of 62 All 62 (JSON)
- 2026P2GNN: Two Prototype Sets to boost GNN Performance10 Mar 2026
- 2025GraphTARIF: Linear Graph Transformer with Augmented Rank and Improved Focus12 Oct 2025
- 2025Analyzing the Effect of Embedding Norms and Singular Values to Oversmoothing in Graph Neural Networks7 Oct 2025
- 2025Virtual Nodes based Heterogeneous Graph Convolutional Neural Network for Efficient Long-Range Information Aggregation28 Sep 2025
- 2025Exploring Heterophily in Graph-level Tasks23 Sep 2025
- 2024Scale-aware Message Passing For Graph Node Classification28 Nov 2024
- 2024Learning From Graph-Structured Data: Addressing Design Issues and Exploring Practical Applications in Graph Representation Learning9 Nov 2024
- 2024Partially Trained Graph Convolutional Networks Resist Oversmoothing17 Oct 2024
- 2024Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learning15 Sep 2024
- 2024Graph Neural Networks for Parkinsons Disease Detection12 Sep 2024
- 2024Revealing the Pitfalls and Re-Evaluating the Advancement of Heterophilic Graph Learning9 Sep 2024
- 2024Foundations and Frontiers of Graph Learning Theory3 Jul 2024
38 more
- 2024Structure-Aware Consensus Network on Graphs with Few Labeled Nodes2 Jul 2024
- 2024What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks27 Jun 2024
- 2024GCEPNet: Graph Convolution-Enhanced Expectation Propagation for Massive MIMO Detection23 Apr 2024
- 2024Representation Learning on Heterophilic Graph with Directional Neighborhood Attention3 Mar 2024
- 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering22 Dec 2023
- 2023Curriculum-Enhanced Residual Soft An-Isotropic Normalization for Over-smoothness in Deep GNNs13 Dec 2023
- 2023Dirichlet Energy Enhancement of Graph Neural Networks by Framelet Augmentation9 Nov 2023
- 2023Language is All a Graph Needs14 Aug 2023
- 2023Theater Aid System for the Visually Impaired Through Transfer Learning of Spatio-Temporal Graph Convolution Networks28 Jun 2023
- 2023On Addressing the Limitations of Graph Neural Networks22 Jun 2023
- 2023Clarify Confused Nodes via Separated Learning4 Jun 2023
- 2023A Fractional Graph Laplacian Approach to Oversmoothing22 May 2023
- 2023MUDiff: Unified Diffusion for Complete Molecule Generation28 Apr 2023
- 2023When Do Graph Neural Networks Help with Node Classification? Investigating the Impact of Homophily Principle on Node Distinguishability25 Apr 2023
- 2023Distributional Signals for Node Classification in Graph Neural Networks7 Apr 2023
- 2023Transformer and Snowball Graph Convolution Learning for Brain functional network Classification28 Mar 2023
- 2023Neighborhood Homophily-based Graph Convolutional Network24 Jan 2023
- 2023Multitask Weakly Supervised Learning for Origin Destination Travel Time Estimation13 Jan 2023
- 2023Reducing Over-smoothing in Graph Neural Networks Using Relational Embeddings7 Jan 2023
- 2022Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networks21 Dec 2022
- 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature28 Nov 2022
- 2022When Do We Need Graph Neural Networks for Node Classification?30 Oct 2022
- 2022Overlapping Community Detection using Dynamic Dilated Aggregation in Deep Residual GCN20 Oct 2022
- 2022Revisiting Heterophily For Graph Neural Networks14 Oct 2022
- 2022GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomials30 Sep 2022
- 2022A Simple Way to Learn Metrics Between Attributed Graphs26 Sep 2022
- 2022Learnable Filters for Geometric Scattering Modules15 Aug 2022
- 2022Affinity-Aware Graph Networks23 Jun 2022
- 2022Skeleton-based Action Recognition via Temporal-Channel Aggregation31 May 2022
- 2022Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey24 May 2022
- 2022KGNN: Distributed Framework for Graph Neural Knowledge Representation17 May 2022
- 2022LEReg: Empower Graph Neural Networks with Local Energy Regularization20 Mar 2022
- 2022Rewiring with Positional Encodings for Graph Neural Networks29 Jan 2022
- 2022Decoupling the Depth and Scope of Graph Neural Networks19 Jan 2022
- 2021Set Twister for Single-hop Node Classification17 Dec 2021
- 2021Multi-scale Graph Convolutional Networks with Self-Attention4 Dec 2021
- 2021SStaGCN: Simplified stacking based graph convolutional networks16 Nov 2021
- 2021Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoods8 Nov 2021
50 newest of 62 All 62 (JSON)
- 2023Language is All a Graph Needscited by 219
- 2022Revisiting Heterophily For Graph Neural Networkscited by 169
- 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
- 2022Decoupling the Depth and Scope of Graph Neural Networkscited by 94
- 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
- 2021Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoodscited by 57
- 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
- 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
- 2021Sampling methods for efficient training of graph convolutional networks: A surveycited by 40
- 2021Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Studycited by 36
- 2022Rewiring with Positional Encodings for Graph Neural Networkscited by 35
- 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
12 most cited of 62 All 62 (JSON)
- 2026P2GNN: Two Prototype Sets to boost GNN Performance10 Mar 2026
- 2025GraphTARIF: Linear Graph Transformer with Augmented Rank and Improved Focus12 Oct 2025
- 2025Analyzing the Effect of Embedding Norms and Singular Values to Oversmoothing in Graph Neural Networks7 Oct 2025
- 2025Virtual Nodes based Heterogeneous Graph Convolutional Neural Network for Efficient Long-Range Information Aggregation28 Sep 2025
- 2025Exploring Heterophily in Graph-level Tasks23 Sep 2025
- 2024Scale-aware Message Passing For Graph Node Classification28 Nov 2024
- 2024Learning From Graph-Structured Data: Addressing Design Issues and Exploring Practical Applications in Graph Representation Learning9 Nov 2024
- 2024Partially Trained Graph Convolutional Networks Resist Oversmoothing17 Oct 2024
- 2024Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learning15 Sep 2024
- 2024Graph Neural Networks for Parkinsons Disease Detection12 Sep 2024
- 2024Revealing the Pitfalls and Re-Evaluating the Advancement of Heterophilic Graph Learning9 Sep 2024
- 2024Foundations and Frontiers of Graph Learning Theory3 Jul 2024
12 newest of 62 All 62 (JSON)