# Tired of Over-smoothing? Stress Graph Drawing Is All You Need!

arXiv: https://arxiv.org/abs/2211.10579 · HTML: https://mlsanity.com/paper/2211.10579/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## Builds on (most cited first, 23 of 23)

- [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)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (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)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Towards Deeper Graph Neural Networks with Differentiable Group Normalization](https://mlsanity.com/paper/2006.06972/) (2020)
- [Learning Graph-Level Representation for Drug Discovery](https://mlsanity.com/paper/1709.03741/) (2017)
- [Graph Classification via Deep Learning with Virtual Nodes](https://mlsanity.com/paper/1708.04357/) (2017)
- [Understanding Isomorphism Bias in Graph Data Sets](https://mlsanity.com/paper/1910.12091/) (2019)
- [A Sparse Stress Model](https://mlsanity.com/paper/1608.08909/) (2016)
- [Understanding the Message Passing in Graph Neural Networks via Power Iteration Clustering](https://mlsanity.com/paper/2006.00144/) (2020)
- [Over-smoothing Effect of Graph Convolutional Networks](https://mlsanity.com/paper/2201.12830/) (2022)

## Abstract (arXiv)

In designing and applying graph neural networks, we often fall into some optimization pitfalls, the most deceptive of which is that we can only build a deep model by solving over-smoothing. The fundamental reason is that we do not understand how graph neural networks work. Stress graph drawing can offer a unique viewpoint to message iteration in the graph, such as the root of the over-smoothing problem lies in the inability of graph models to maintain an ideal distance between nodes. We further elucidate the trigger conditions of over-smoothing and propose Stress Graph Neural Networks. By introducing the attractive and repulsive message passing from stress iteration, we show how to build a deep model without preventing over-smoothing, how to use repulsive information, and how to optimize the current message-passing scheme to approximate the full stress message propagation. By performing different tasks on 23 datasets, we verified the effectiveness of our attractive and repulsive models and the derived relationship between stress iteration and graph neural networks. We believe that stress graph drawing will be a popular resource for understanding and designing graph neural networks.