# Tackling Over-Smoothing for General Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2008.09864 · HTML: https://mlsanity.com/paper/2008.09864/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2020.

## Built on by (most cited first, 30 of 66)

- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
- [DiffWire: Inductive Graph Rewiring via the Lov'asz Bound](https://mlsanity.com/paper/2206.07369/) (2022)
- [Revisiting Over-smoothing in BERT from the Perspective of Graph](https://mlsanity.com/paper/2202.08625/) (2022)
- [On Provable Benefits of Depth in Training Graph Convolutional Networks](https://mlsanity.com/paper/2110.15174/) (2021)
- [Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoods](https://mlsanity.com/paper/2111.04840/) (2021)
- [A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2212.10701/) (2022)
- [GPGait: Generalized Pose-based Gait Recognition](https://mlsanity.com/paper/2303.05234/) (2023)
- [Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Study](https://mlsanity.com/paper/2108.10521/) (2021)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [A New Perspective on the Effects of Spectrum in Graph Neural Networks](https://mlsanity.com/paper/2112.07160/) (2021)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning](https://mlsanity.com/paper/2505.15547/) (2025)
- [Subgraph Pooling: Tackling Negative Transfer on Graphs](https://mlsanity.com/paper/2402.08907/) (2024)
- [A Comprehensive Survey on Distributed Training of Graph Neural Networks](https://mlsanity.com/paper/2211.05368/) (2022)
- [EquiPocket: an E(3)-Equivariant Geometric Graph Neural Network for Ligand Binding Site Prediction](https://mlsanity.com/paper/2302.12177/) (2023)
- [MacDiff: Unified Skeleton Modeling with Masked Conditional Diffusion](https://mlsanity.com/paper/2409.10473/) (2024)
- [Towards Deepening Graph Neural Networks: A GNTK-based Optimization Perspective](https://mlsanity.com/paper/2103.03113/) (2021)
- [Unifying Graph Contrastive Learning with Flexible Contextual Scopes](https://mlsanity.com/paper/2210.08792/) (2022)
- [You Can Have Better Graph Neural Networks by Not Training Weights at All: Finding Untrained GNNs Tickets](https://mlsanity.com/paper/2211.15335/) (2022)
- [Improving Expressivity of GNNs with Subgraph-specific Factor Embedded Normalization](https://mlsanity.com/paper/2305.19903/) (2023)
- [MGDCF: Distance Learning via Markov Graph Diffusion for Neural Collaborative Filtering](https://mlsanity.com/paper/2204.02338/) (2022)
- [Old can be Gold: Better Gradient Flow can Make Vanilla-GCNs Great Again](https://mlsanity.com/paper/2210.08122/) (2022)
- [GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications](https://mlsanity.com/paper/2406.03569/) (2024)
- [Multi-Level Attention Pooling for Graph Neural Networks: Unifying Graph Representations with Multiple Localities](https://mlsanity.com/paper/2103.01488/) (2021)
- [DGDNN: Decoupled Graph Diffusion Neural Network for Stock Movement Prediction](https://mlsanity.com/paper/2401.01846/) (2024)
- [Are We Measuring Oversmoothing in Graph Neural Networks Correctly?](https://mlsanity.com/paper/2502.04591/) (2025)

## Abstract (arXiv)

Increasing the depth of GCN, which is expected to permit more expressivity, is shown to incur performance detriment especially on node classification. The main cause of this lies in over-smoothing. The over-smoothing issue drives the output of GCN towards a space that contains limited distinguished information among nodes, leading to poor expressivity. Several works on refining the architecture of deep GCN have been proposed, but it is still unknown in theory whether or not these refinements are able to relieve over-smoothing. In this paper, we first theoretically analyze how general GCNs act with the increase in depth, including generic GCN, GCN with bias, ResGCN, and APPNP. We find that all these models are characterized by a universal process: all nodes converging to a cuboid. Upon this theorem, we propose DropEdge to alleviate over-smoothing by randomly removing a certain number of edges at each training epoch. Theoretically, DropEdge either reduces the convergence speed of over-smoothing or relieves the information loss caused by dimension collapse. Experimental evaluations on simulated dataset have visualized the difference in over-smoothing between different GCNs. Moreover, extensive experiments on several real benchmarks support that DropEdge consistently improves the performance on a variety of both shallow and deep GCNs.