# On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems

arXiv: https://arxiv.org/abs/2405.01009 · HTML: https://mlsanity.com/paper/2405.01009/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 57 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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 Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [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)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [DRew: Dynamically Rewired Message Passing with Delay](https://mlsanity.com/paper/2305.08018/) (2023)

## Built on by (most cited first, 28 of 28)

- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning](https://mlsanity.com/paper/2505.15547/) (2025)
- [Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks](https://mlsanity.com/paper/2506.07624/) (2025)
- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [Can You Hear Me Now? A Benchmark for Long-Range Graph Propagation](https://mlsanity.com/paper/2512.17762/) (2025)
- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [Over-squashing in Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2506.15507/) (2025)
- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [FairGE: Fairness-Aware Graph Encoding in Incomplete Social Networks](https://mlsanity.com/paper/2601.09394/) (2026)
- [Interpreting Temporal Graph Neural Networks with Koopman Theory](https://mlsanity.com/paper/2410.13469/) (2024)
- [Early-Exit Graph Neural Networks](https://mlsanity.com/paper/2505.18088/) (2025)
- [Stochastic Parroting in Temporal Attention -- Regulating the Diagonal Sink](https://mlsanity.com/paper/2602.10956/) (2026)
- [TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows](https://mlsanity.com/paper/2508.05070/) (2025)
- [Wavy Transformer](https://mlsanity.com/paper/2508.12787/) (2025)
- [gLSTM: Mitigating Over-Squashing by Increasing Storage Capacity](https://mlsanity.com/paper/2510.08450/) (2025)
- [From Message-Passing to Linearized Graph Sequence Models](https://mlsanity.com/paper/2605.12358/) (2026)
- [Information propagation dynamics in Deep Graph Networks](https://mlsanity.com/paper/2410.10464/) (2024)
- [Non-Dissipative Graph Propagation for Non-Local Community Detection](https://mlsanity.com/paper/2508.14097/) (2025)
- [Asynchronous Message Passing for Addressing Oversquashing in Graph Neural Networks](https://mlsanity.com/paper/2509.06777/) (2025)
- [Model Metamers Reveal Invariances in Graph Neural Networks](https://mlsanity.com/paper/2510.17378/) (2025)
- [How Wide and How Deep? Mitigating Over-Squashing of GNNs via Channel Capacity Constrained Estimation](https://mlsanity.com/paper/2511.06443/) (2025)
- [Geometry-Induced Diffusion on Graphs: A Learnable Weighted Laplacian for Spectral GNNs](https://mlsanity.com/paper/2602.18141/) (2026)
- [Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables](https://mlsanity.com/paper/2605.13383/) (2026)
- [Graph Hierarchical Recurrence for Long-Range Generalization](https://mlsanity.com/paper/2605.18387/) (2026)
- [Universal Transformers for Circuit Computations: Perfect Length Generalization in Tiny Transformers](https://mlsanity.com/paper/2608.31067/) (2026)
- [TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networks](https://mlsanity.com/paper/2609.32940/) (2026)
- [Get a GRIP, this will be a long TRIP: A Quantifiable Long-Range Framework for Verifying Over-squashing](https://mlsanity.com/paper/2610.03556/) (2026)
- [Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective](https://mlsanity.com/paper/2610.04157/) (2026)

## Abstract (arXiv)

A common problem in Message-Passing Neural Networks is oversquashing -- the limited ability to facilitate effective information flow between distant nodes. Oversquashing is attributed to the exponential decay in information transmission as node distances increase. This paper introduces a novel perspective to address oversquashing, leveraging dynamical systems properties of global and local non-dissipativity, that enable the maintenance of a constant information flow rate. We present SWAN, a uniquely parameterized GNN model with antisymmetry both in space and weight domains, as a means to obtain non-dissipativity. Our theoretical analysis asserts that by implementing these properties, SWAN offers an enhanced ability to transmit information over extended distances. Empirical evaluations on synthetic and real-world benchmarks that emphasize long-range interactions validate the theoretical understanding of SWAN, and its ability to mitigate oversquashing.