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On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems
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Proposes SWAN, a DE-GNN with space and weight antisymmetry that is globally and locally non-dissipative, giving a constant information flow rate to mitigate oversquashing.
Problem
Oversquashing in message-passing GNNs, where information transfer between distant nodes decays exponentially with distance, hindering long-range interaction modeling.
Approach
Extends ADGN's node-wise weight antisymmetry with a graph-level space antisymmetry term (antisymmetric graph shift operator), so the graph-wide Jacobian has purely imaginary eigenvalues; this yields constant (non-decaying) information propagation across layers and nodes.
Key results
- SWAN-LEARN achieves log10(MSE) of -0.5981 on diameter and -0.0739 on eccentricity, the best among compared models, with improvements of up to 117% over the runner-up on graph property prediction.
- On Peptides-func, SWAN-LEARN reaches 67.51 AP versus 65.35 for GraphGPS+LapPE and 59.75 for ADGN.
- On Peptides-struct, SWAN-LEARN achieves MAE 0.2485, the best among reported models.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learn the aggregation operators | SWAN · Peptides-func | average precision: 63.13$_{\pm0.46}$ -> 67.51$_{\pm0.39}$ | Helped |
| Learn the aggregation operators | SWAN · Peptides-struct | MAE: 0.2571$_{\pm0.0018}$ -> 0.2485$_{\pm0.0009}$ | Helped |
| Learn the aggregation operators | SWAN · PascalVOC-sp | macro-weighted F1: 27.96$_{\pm0.48}$ -> 31.92$_{\pm2.50}$ | Mixed |
| Learn the aggregation operators | SWAN · Graph Property Prediction | log10(MSE): Diameter: -0.5249$_{\pm0.0155}$ -> -0.5981$_{\pm0.1145}$; SSSP: -3.2370$_{\pm0.0834}$ -> -3.5425$_{\pm0.0830}$; Eccentri | Helped |
| Add spatial antisymmetry (use beta instead of beta=0) (ablation) | SWAN · Peptides-func | average precision: 61.95$_{\pm00.67}$ -> 63.13$_{\pm0.46}$ | Helped |
| Add spatial antisymmetry (use beta instead of beta=0) (ablation) | SWAN · Peptides-struct | MAE: 0.2703$_{\pm0.0023}$ -> 0.2571$_{\pm0.0018}$ | Helped |
| Add spatial antisymmetry (use beta instead of beta=0) (ablation) | SWAN · Graph Property Prediction | log10(MSE): Diameter: -0.3882$_{\pm0.0610}$ -> -0.5249$_{\pm0.0155}$; SSSP: -3.2061$_{\pm0.0416}$ -> -3.2370$_{\pm0.0834}$; Eccentri | Mixed |
| Enforce antisymmetric V instead of using unconstrained V (ablation) | SWAN · Peptides-func | average precision: 61.19$_{\pm0.37}$ -> 63.13$_{\pm0.46}$ | Helped |
| Enforce antisymmetric V instead of using unconstrained V (ablation) | SWAN · Peptides-struct | MAE: 0.2672$_{\pm0.0012}$ -> 0.2571$_{\pm0.0018}$ | Helped |
| Enforce antisymmetric V instead of using unconstrained V (ablation) | SWAN · Graph Property Prediction | log10(MSE): Diameter: -0.5497$_{\pm0.0766}$ -> -0.5249$_{\pm0.0155}$; SSSP: -3.1913$_{\pm0.0762}$ -> -3.2370$_{\pm0.0834}$; Eccentri | Mixed |
Surprising findings
- Weight-antisymmetry-only variant (SWAN_beta=0) performs worse than full SWAN, indicating spatial antisymmetry adds benefit.
- On PascalVOC-sp, GraphGPS+LapPE (37.48 F1) outperforms SWAN variants, so SWAN does not win on all real-world benchmarks.
Limitations
- Forward Euler discretization is unstable for purely imaginary eigenvalues, requiring a stabilizing constant gamma and small step sizes.
- Assumes the Jacobian does not change significantly over time, justified only numerically in an appendix.
- Does not outperform graph transformers such as GraphGPS on PascalVOC-sp.
Experimental setup
Datasets: Graph transfer synthetic (line, ring, crossed-ring) Graph property prediction synthetic (diameter, SSSP, eccentricity) Peptides-func Peptides-struct PascalVOC-sp
Benchmarks: Graph transfer (line, ring, crossed-ring; k=3,5,10,50) Diameter SSSP Eccentricity Peptides-func Peptides-struct PascalVOC-sp
Metrics: MSE (log10) average precision MAE macro F1
Baselines: GCN GraphSAGE GAT GatedGCN GIN GINE GCNII DGC GRAND GraphCON ADGN SAN
Builds on: ADGN GraphCON GRAND DGC
Closest papers by meaning
- Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables (NeurIPS 2026 · similarity 0.88)
- A Dynamical Systems-Inspired Pruning Strategy for Addressing Oversmoothing in Graph Attention Networks (ICML 2025 · similarity 0.87)
- Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models (NeurIPS 2025 · similarity 0.87)
- Understanding Virtual Nodes: Oversquashing and Node Heterogeneity (ICLR 2025 · similarity 0.87)
- Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching (ICML 2025 · similarity 0.86)
- Graph Neural Networks Do Not Always Oversmooth (NeurIPS 2024 · similarity 0.86)
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