# On the Equivalence of Decoupled Graph Convolution Network and Label Propagation

arXiv: https://arxiv.org/abs/2010.12408 · HTML: https://mlsanity.com/paper/2010.12408/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 30 of 49)

- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [NRGNN: Learning a Label Noise-Resistant Graph Neural Network on Sparsely and Noisily Labeled Graphs](https://mlsanity.com/paper/2106.04714/) (2021)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm](https://mlsanity.com/paper/2203.00638/) (2022)
- [Meta Propagation Networks for Graph Few-shot Semi-supervised Learning](https://mlsanity.com/paper/2112.09810/) (2021)
- [Towards Deep Attention in Graph Neural Networks: Problems and Remedies](https://mlsanity.com/paper/2306.02376/) (2023)
- [RIM: Reliable Influence-based Active Learning on Graphs](https://mlsanity.com/paper/2110.14854/) (2021)
- [Noise-robust Graph Learning by Estimating and Leveraging Pairwise Interactions](https://mlsanity.com/paper/2106.07451/) (2021)
- [Topology-aware Embedding Memory for Continual Learning on Expanding Networks](https://mlsanity.com/paper/2401.13200/) (2024)
- [Investigating Out-of-Distribution Generalization of GNNs: An Architecture Perspective](https://mlsanity.com/paper/2402.08228/) (2024)
- [Toward Robust Graph Semi-Supervised Learning against Extreme Data Scarcity](https://mlsanity.com/paper/2208.12422/) (2022)
- [ERASE: Error-Resilient Representation Learning on Graphs for Label Noise Tolerance](https://mlsanity.com/paper/2312.08852/) (2023)
- [DPAR: Decoupled Graph Neural Networks with Node-Level Differential Privacy](https://mlsanity.com/paper/2210.04442/) (2022)
- [Domain-adaptive Message Passing Graph Neural Network](https://mlsanity.com/paper/2308.16470/) (2023)
- [Neighborhood-Enhanced Supervised Contrastive Learning for Collaborative Filtering](https://mlsanity.com/paper/2402.11523/) (2024)
- [Label Propagation with Weak Supervision](https://mlsanity.com/paper/2210.03594/) (2022)
- [Homophily-enhanced Structure Learning for Graph Clustering](https://mlsanity.com/paper/2308.05309/) (2023)
- [PSL: Rethinking and Improving Softmax Loss from Pairwise Perspective for Recommendation](https://mlsanity.com/paper/2411.00163/) (2024)
- [Dynamic Graph Transformer with Correlated Spatial-Temporal Positional Encoding](https://mlsanity.com/paper/2407.16959/) (2024)
- [Multi-View Subgraph Neural Networks: Self-Supervised Learning with Scarce Labeled Data](https://mlsanity.com/paper/2404.12569/) (2024)
- [NTFormer: A Composite Node Tokenized Graph Transformer for Node Classification](https://mlsanity.com/paper/2406.19249/) (2024)
- [Alternately Optimized Graph Neural Networks](https://mlsanity.com/paper/2206.03638/) (2022)
- [Tokenized Graph Transformer with Neighborhood Augmentation for Node Classification in Large Graphs](https://mlsanity.com/paper/2305.12677/) (2023)
- [Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networks](https://mlsanity.com/paper/2411.02279/) (2024)
- [Uncertainty-Aware Graph Structure Learning](https://mlsanity.com/paper/2502.12618/) (2025)
- [Diffusion Probabilistic Models for Structured Node Classification](https://mlsanity.com/paper/2302.10506/) (2023)
- [Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian](https://mlsanity.com/paper/2401.07463/) (2024)
- [Decoupled Subgraph Federated Learning](https://mlsanity.com/paper/2402.19163/) (2024)

## Abstract (arXiv)

The original design of Graph Convolution Network (GCN) couples feature transformation and neighborhood aggregation for node representation learning. Recently, some work shows that coupling is inferior to decoupling, which supports deep graph propagation better and has become the latest paradigm of GCN (e.g., APPNP and SGCN). Despite effectiveness, the working mechanisms of the decoupled GCN are not well understood. In this paper, we explore the decoupled GCN for semi-supervised node classification from a novel and fundamental perspective -- label propagation. We conduct thorough theoretical analyses, proving that the decoupled GCN is essentially the same as the two-step label propagation: first, propagating the known labels along the graph to generate pseudo-labels for the unlabeled nodes, and second, training normal neural network classifiers on the augmented pseudo-labeled data. More interestingly, we reveal the effectiveness of decoupled GCN: going beyond the conventional label propagation, it could automatically assign structure- and model- aware weights to the pseudo-label data. This explains why the decoupled GCN is relatively robust to the structure noise and over-smoothing, but sensitive to the label noise and model initialization. Based on this insight, we propose a new label propagation method named Propagation then Training Adaptively (PTA), which overcomes the flaws of the decoupled GCN with a dynamic and adaptive weighting strategy. Our PTA is simple yet more effective and robust than decoupled GCN. We empirically validate our findings on four benchmark datasets, demonstrating the advantages of our method. The code is available at https://github.com/DongHande/PT_propagation_then_training.