Data to 7 Oct 2026

Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning

arXiv 1801.07606 ↗First posted 22 Jan 2018cs.LG stat.MLcited by 1,099

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Abstract (arXiv)

Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires a considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of over-smoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches significantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have verified our theory and proposals.

Key facts. Cited by 1,099 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Jan 2018.

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Citing papers per year: 2021: 216; 2022: 220; 2023: 211; 2024: 162; 2025: 153; 2026: 137.

1,099 papers.

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2021How Attentive are Graph Attention Networks?cited by 818
2021Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Predictioncited by 273
2021Combinatorial optimization and reasoning with graph neural networkscited by 267
2021A Survey on Deep Semi-supervised Learningcited by 250
2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
2021Spatial-Temporal Graph ODE Networks for Traffic Flow Forecastingcited by 209
2021CodeNet: A Large-Scale AI for Code Dataset for Learning a Diversity of Coding Taskscited by 199
2022Representing Long-Range Context for Graph Neural Networks with Global Attentioncited by 193
2022Structure-Aware Transformer for Graph Representation Learningcited by 191
2022Pure Transformers are Powerful Graph Learnerscited by 188
2022Rethinking Graph Neural Networks for Anomaly Detectioncited by 185

38 more

2022Vision GNN: An Image is Worth Graph of Nodescited by 185
2021Self-Supervised Learning of Graph Neural Networks: A Unified Reviewcited by 184
2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
2022Graph neural networks for materials science and chemistrycited by 181
2021Are we really making much progress? Revisiting, benchmarking, and refining heterogeneous graph neural networkscited by 176
2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
2021Training Graph Neural Networks with 1000 Layerscited by 169
2023Graph Inductive Biases in Transformers without Message Passingcited by 150
2022Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphscited by 144
2023Do We Really Need Complicated Model Architectures For Temporal Networks?cited by 141
2021From Canonical Correlation Analysis to Self-supervised Graph Neural Networkscited by 138
2021Self-supervised Learning on Graphs: Contrastive, Generative,or Predictivecited by 136
2022Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practicecited by 136
2022Data Augmentation for Deep Graph Learning: A Surveycited by 132
2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
2022AEGNN: Asynchronous Event-based Graph Neural Networkscited by 118
2021An Empirical Study of Graph Contrastive Learningcited by 113
2021Learning Graph Embeddings for Compositional Zero-shot Learningcited by 112
2021SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networkscited by 108
2022Not too little, not too much: a theoretical analysis of graph (over)smoothingcited by 106
2022FoSR: First-order spectral rewiring for addressing oversquashing in GNNscited by 104
2023Graph Foundation Models: Concepts, Opportunities and Challengescited by 101
2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
2022Decoupling the Depth and Scope of Graph Neural Networkscited by 94
2022MultiScale MeshGraphNetscited by 94
2021Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibrationcited by 91
2024Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classificationcited by 83
2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
2022Graph Attention Multi-Layer Perceptroncited by 82
2023Attending to Graph Transformerscited by 81
2021Graph-based Semi-supervised Learning: A Comprehensive Reviewcited by 79
2022DiffWire: Inductive Graph Rewiring via the Lov'asz Boundcited by 79
2023Graph-ToolFormer: To Empower LLMs with Graph Reasoning Ability via Prompt Augmented by ChatGPTcited by 78
2021Towards Self-Explainable Graph Neural Networkcited by 75
2021BertGCN: Transductive Text Classification by Combining GCN and BERTcited by 74
2021NRGNN: Learning a Label Noise-Resistant Graph Neural Network on Sparsely and Noisily Labeled Graphscited by 73

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