# A Survey on Oversmoothing in Graph Neural Networks

arXiv: https://arxiv.org/abs/2303.10993 · HTML: https://mlsanity.com/paper/2303.10993/

## Key facts

- Cited by 247 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)

## Built on by (most cited first, 30 of 247)

- [Large Language Models on Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2312.02783/) (2023)
- [Graph Mamba: Towards Learning on Graphs with State Space Models](https://mlsanity.com/paper/2402.08678/) (2024)
- [CARTE: Pretraining and Transfer for Tabular Learning](https://mlsanity.com/paper/2402.16785/) (2024)
- [How does over-squashing affect the power of GNNs?](https://mlsanity.com/paper/2306.03589/) (2023)
- [Demystifying Oversmoothing in Attention-Based Graph Neural Networks](https://mlsanity.com/paper/2305.16102/) (2023)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNs](https://mlsanity.com/paper/2406.02997/) (2024)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching](https://mlsanity.com/paper/2312.16560/) (2023)
- [Spectral Graph Pruning Against Over-Squashing and Over-Smoothing](https://mlsanity.com/paper/2404.04612/) (2024)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations](https://mlsanity.com/paper/2407.19916/) (2024)
- [Over-Squashing in Graph Neural Networks: A Comprehensive survey](https://mlsanity.com/paper/2308.15568/) (2023)
- [Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges](https://mlsanity.com/paper/2311.07073/) (2023)
- [Setting the Record Straight on Transformer Oversmoothing](https://mlsanity.com/paper/2401.04301/) (2024)
- [Cayley Graph Propagation](https://mlsanity.com/paper/2410.03424/) (2024)
- [Graph Meets LLMs: Towards Large Graph Models](https://mlsanity.com/paper/2308.14522/) (2023)
- [Towards Quantifying Long-Range Interactions in Graph Machine Learning: a Large Graph Dataset and a Measurement](https://mlsanity.com/paper/2503.09008/) (2025)
- [Permutation Equivariant Graph Framelets for Heterophilous Graph Learning](https://mlsanity.com/paper/2306.04265/) (2023)
- [Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning](https://mlsanity.com/paper/2505.15547/) (2025)
- [Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks](https://mlsanity.com/paper/2308.16800/) (2023)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks](https://mlsanity.com/paper/2308.01602/) (2023)
- [GraphGPT: Generative Pre-trained Graph Eulerian Transformer](https://mlsanity.com/paper/2401.00529/) (2023)
- [Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling](https://mlsanity.com/paper/2402.10634/) (2024)
- [Segment Anything in Non-Euclidean Domains: Challenges and Opportunities](https://mlsanity.com/paper/2304.11595/) (2023)

## Abstract (arXiv)

Node features of graph neural networks (GNNs) tend to become more similar with the increase of the network depth. This effect is known as over-smoothing, which we axiomatically define as the exponential convergence of suitable similarity measures on the node features. Our definition unifies previous approaches and gives rise to new quantitative measures of over-smoothing. Moreover, we empirically demonstrate this behavior for several over-smoothing measures on different graphs (small-, medium-, and large-scale). We also review several approaches for mitigating over-smoothing and empirically test their effectiveness on real-world graph datasets. Through illustrative examples, we demonstrate that mitigating over-smoothing is a necessary but not sufficient condition for building deep GNNs that are expressive on a wide range of graph learning tasks. Finally, we extend our definition of over-smoothing to the rapidly emerging field of continuous-time GNNs.