# Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks

arXiv: https://arxiv.org/abs/2308.16800 · HTML: https://mlsanity.com/paper/2308.16800/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 67 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Builds on (most cited first, 30 of 48)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [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)
- [Representation Degeneration Problem in Training Natural Language Generation Models](https://mlsanity.com/paper/1907.12009/) (2019)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)

## Built on by (most cited first, 18 of 18)

- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Spectral Graph Pruning Against Over-Squashing and Over-Smoothing](https://mlsanity.com/paper/2404.04612/) (2024)
- [Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning](https://mlsanity.com/paper/2505.15547/) (2025)
- [Rethinking Functional Brain Connectome Analysis: Do Graph Deep Learning Models Help](https://mlsanity.com/paper/2501.17207/) (2025)
- [Only Large Weights (And Not Skip Connections) Can Prevent the Perils of Rank Collapse](https://mlsanity.com/paper/2505.16284/) (2025)
- [Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph](https://mlsanity.com/paper/2409.11504/) (2024)
- [Are We Measuring Oversmoothing in Graph Neural Networks Correctly?](https://mlsanity.com/paper/2502.04591/) (2025)
- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [Simplifying the Theory on Over-Smoothing](https://mlsanity.com/paper/2407.11876/) (2024)
- [Pretraining Graph Transformers with Atom-in-a-Molecule Quantum Properties for Improved ADMET Modeling](https://mlsanity.com/paper/2410.08024/) (2024)
- [On the Relationship Between Robustness and Expressivity of Graph Neural Networks](https://mlsanity.com/paper/2504.13786/) (2025)
- [Generalized Probabilistic Attention Mechanism in Transformers](https://mlsanity.com/paper/2410.15578/) (2024)
- [Position: Don't be Afraid of Over-Smoothing And Over-Squashing](https://mlsanity.com/paper/2601.07419/) (2026)
- [What Can We Learn From MIMO Graph Convolutions?](https://mlsanity.com/paper/2505.11346/) (2025)
- [Distilling Influences to Mitigate Prediction Churn in Graph Neural Networks](https://mlsanity.com/paper/2310.00946/) (2023)
- [Differential Encoding for Improved Representation Learning over Graphs](https://mlsanity.com/paper/2407.02758/) (2024)
- [How Smoothing is N-simplicial Attention?](https://mlsanity.com/paper/2512.15600/) (2025)
- [LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Prediction](https://mlsanity.com/paper/2609.14977/) (2026)

## Abstract (arXiv)

Our study reveals new theoretical insights into over-smoothing and feature over-correlation in graph neural networks. Specifically, we demonstrate that with increased depth, node representations become dominated by a low-dimensional subspace that depends on the aggregation function but not on the feature transformations. For all aggregation functions, the rank of the node representations collapses, resulting in over-smoothing for particular aggregation functions. Our study emphasizes the importance for future research to focus on rank collapse rather than over-smoothing. Guided by our theory, we propose a sum of Kronecker products as a beneficial property that provably prevents over-smoothing, over-correlation, and rank collapse. We empirically demonstrate the shortcomings of existing models in fitting target functions of node classification tasks.