# On the Bottleneck of Graph Neural Networks and its Practical Implications

arXiv: https://arxiv.org/abs/2006.05205 · HTML: https://mlsanity.com/paper/2006.05205/

## Key facts

- Cited by 631 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 30 of 631)

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- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
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- [Exphormer: Sparse Transformers for Graphs](https://mlsanity.com/paper/2303.06147/) (2023)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
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- [Do We Really Need Complicated Model Architectures For Temporal Networks?](https://mlsanity.com/paper/2302.11636/) (2023)
- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
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- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
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- [Rethinking the Expressive Power of GNNs via Graph Biconnectivity](https://mlsanity.com/paper/2301.09505/) (2023)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [Graph Foundation Models: Concepts, Opportunities and Challenges](https://mlsanity.com/paper/2310.11829/) (2023)
- [Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature](https://mlsanity.com/paper/2211.15779/) (2022)

## Abstract (arXiv)

Since the proposal of the graph neural network (GNN) by Gori et al. (2005) and Scarselli et al. (2008), one of the major problems in training GNNs was their struggle to propagate information between distant nodes in the graph. We propose a new explanation for this problem: GNNs are susceptible to a bottleneck when aggregating messages across a long path. This bottleneck causes the over-squashing of exponentially growing information into fixed-size vectors. As a result, GNNs fail to propagate messages originating from distant nodes and perform poorly when the prediction task depends on long-range interaction. In this paper, we highlight the inherent problem of over-squashing in GNNs: we demonstrate that the bottleneck hinders popular GNNs from fitting long-range signals in the training data; we further show that GNNs that absorb incoming edges equally, such as GCN and GIN, are more susceptible to over-squashing than GAT and GGNN; finally, we show that prior work, which extensively tuned GNN models of long-range problems, suffers from over-squashing, and that breaking the bottleneck improves their state-of-the-art results without any tuning or additional weights. Our code is available at https://github.com/tech-srl/bottleneck/ .