# Over-Squashing in GNNs and Causal Inference of Rewiring Strategies

arXiv: https://arxiv.org/abs/2508.09265 · HTML: https://mlsanity.com/paper/2508.09265/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 12 Aug 2025.

## Builds on (most cited first, 22 of 22)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [Understanding Oversquashing in GNNs through the Lens of Effective Resistance](https://mlsanity.com/paper/2302.06835/) (2023)
- [On the Connection Between MPNN and Graph Transformer](https://mlsanity.com/paper/2301.11956/) (2023)
- [k-hop Graph Neural Networks](https://mlsanity.com/paper/1907.06051/) (2019)
- [Locality-Aware Graph-Rewiring in GNNs](https://mlsanity.com/paper/2310.01668/) (2023)
- [Shortest Path Networks for Graph Property Prediction](https://mlsanity.com/paper/2206.01003/) (2022)
- [Simplifying Subgraph Representation Learning for Scalable Link Prediction](https://mlsanity.com/paper/2301.12562/) (2023)
- [Scalable Expressiveness through Preprocessed Graph Perturbations](https://mlsanity.com/paper/2406.11714/) (2024)

## Built on by (most cited first, 1 of 1)

- [Graph Rewiring in GNNs to Mitigate Over-Squashing and Over-Smoothing: A Survey](https://mlsanity.com/paper/2605.00951/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have exhibited state-of-the-art performance across wide-range of domains such as recommender systems, material design, and drug repurposing. Yet message-passing GNNs suffer from over-squashing -- exponential compression of long-range information from distant nodes -- which limits expressivity. Rewiring techniques can ease this bottleneck; but their practical impacts are unclear due to the lack of a direct empirical over-squashing metric. We propose a rigorous, topology-focused method for assessing over-squashing between node pairs using the decay rate of their mutual sensitivity. We then extend these pairwise assessments to four graph-level statistics (prevalence, intensity, variability, extremity). Coupling these metrics with a within-graph causal design, we quantify how rewiring strategies affect over-squashing on diverse graph- and node-classification benchmarks. Our extensive empirical analyses show that most graph classification datasets suffer from over-squashing (but to various extents), and rewiring effectively mitigates it -- though the degree of mitigation, and its translation into performance gains, varies by dataset and method. We also found that over-squashing is less notable in node classification datasets, where rewiring often increases over-squashing, and performance variations are uncorrelated with over-squashing changes. These findings suggest that rewiring is most beneficial when over-squashing is both substantial and corrected with restraint -- while overly aggressive rewiring, or rewiring applied to minimally over-squashed graphs, is unlikely to help and may even harm performance. Our plug-and-play diagnostic tool lets practitioners decide -- before any training -- whether rewiring is likely to pay off.