mlsanityData to 7 Oct 2026

Anti-Symmetric DGN: a stable architecture for Deep Graph Networks

arXiv 2210.09789 ↗First posted 18 Oct 2022cs.LGcited by 58

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Abstract (arXiv)

Deep Graph Networks (DGNs) currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in their ability to propagate and preserve long-term dependencies between nodes, i.e., they suffer from the over-squashing phenomena. This reduces their effectiveness, since predictive problems may require to capture interactions at different, and possibly large, radii in order to be effectively solved. In this work, we present Anti-Symmetric Deep Graph Networks (A-DGNs), a framework for stable and non-dissipative DGN design, conceived through the lens of ordinary differential equations. We give theoretical proof that our method is stable and non-dissipative, leading to two key results: long-range information between nodes is preserved, and no gradient vanishing or explosion occurs in training. We empirically validate the proposed approach on several graph benchmarks, showing that A-DGN yields to improved performance and enables to learn effectively even when dozens of layers are used.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). Builds on 34 of its 46 references that are in the map. First posted on arXiv 18 Oct 2022.

Builds on

34 of 46 references.

References · 34

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  7. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  8. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  9. 2019Simplifying Graph Convolutional Networkscited by 1,470
  10. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  11. 2019Strategies for Pre-training Graph Neural Networkscited by 964
  12. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
22 more
  1. 2020Simple and Deep Graph Convolutional Networkscited by 857
  2. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  3. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 624
  4. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
  5. 2020Principal Neighbourhood Aggregation for Graph Netscited by 477
  6. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  7. 2017Stable Architectures for Deep Neural Networkscited by 340
  8. 2021GRAND: Graph Neural Diffusioncited by 258
  9. 2018Modeling polypharmacy side effects with graph convolutional networkscited by 237
  10. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  11. 2019Graph Neural Ordinary Differential Equationscited by 153
  12. 2021ETA Prediction with Graph Neural Networks in Google Mapscited by 130
  13. 2022Graph-Coupled Oscillator Networkscited by 123
  14. 2019Fake News Detection on Social Media using Geometric Deep Learningcited by 115
  15. 2019AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networkscited by 112
  16. 2019A Gentle Introduction to Deep Learning for Graphscited by 107
  17. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  18. 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
  19. 2017Reversible Architectures for Arbitrarily Deep Residual Neural Networkscited by 69
  20. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  21. 2022pathGCN: Learning General Graph Spatial Operators from Pathscited by 15
  22. 2022Euler State Networks: Non-dissipative Reservoir Computingcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 10; 2024: 18; 2025: 18; 2026: 12.

58 papers.

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  1. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 42
  2. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  3. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  4. 2024Long Range Propagation on Continuous-Time Dynamic Graphscited by 26
  5. 2023Towards Deep Attention in Graph Neural Networks: Problems and Remediescited by 24
  6. 2023Over-Squashing in Graph Neural Networks: A Comprehensive surveycited by 23
  7. 2023Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreachingcited by 23
  8. 2023Deep learning for dynamic graphs: models and benchmarkscited by 19
  9. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  10. 2023Feature Transportation Improves Graph Neural Networkscited by 15
  11. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  12. 2025Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Taskscited by 12
38 more
  1. 2024Temporal Graph ODEs for Irregularly-Sampled Time Seriescited by 11
  2. 2025Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspectivecited by 10
  3. 2024On The Temporal Domain of Differential Equation Inspired Graph Neural Networkscited by 9
  4. 2024Feature Distribution on Graph Topology Mediates the Effect of Graph Convolution: Homophily Perspectivecited by 9
  5. 2025Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modelingcited by 9
  6. 2024Towards Generalizability of Multi-Agent Reinforcement Learning in Graphs with Recurrent Message Passingcited by 8
  7. 2025Can You Hear Me Now? A Benchmark for Long-Range Graph Propagationcited by 8
  8. 2023Supercharging Graph Transformers with Advective Diffusioncited by 7
  9. 2024Graph Neural Reaction Diffusion Modelscited by 6
  10. 2025Over-squashing in Spatiotemporal Graph Neural Networkscited by 6
  11. 2025Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamicscited by 6
  12. 2023Investigating the Interplay between Features and Structures in Graph Learningcited by 5
  13. 2025Neural Variable-Order Fractional Differential Equation Networkscited by 5
  14. 2023Transformers are efficient hierarchical chemical graph learnerscited by 4
  15. 2024SAGMAN: Stability Analysis of Graph Neural Networks on the Manifoldscited by 4
  16. 2025Efficient Training of Neural Fractional-Order Differential Equation via Adjoint Backpropagationcited by 3
  17. 2024Towards Data-Centric Automatic R&Dcited by 2
  18. 2024Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusioncited by 2
  19. 2024Scalable Graph Compressed Convolutionscited by 2
  20. 2025Early-Exit Graph Neural Networkscited by 2
  21. 2025Structured Transformations for Stable and Interpretable Neural Computationcited by 2
  22. 2026Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passingcited by 2
  23. 2023Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networkscited by 1
  24. 2024Link Prediction with Physics-Inspired Graph Neural Networkscited by 1
  25. 2024Conditional Shift-Robust Conformal Prediction for Graph Neural Networkcited by 1
  26. 2025Understanding Learning Dynamics Through Structured Representationscited by 1
  27. 2025gLSTM: Mitigating Over-Squashing by Increasing Storage Capacitycited by 1
  28. 2026From Message-Passing to Linearized Graph Sequence Modelscited by 1
  29. 2024Lying Graph Convolution: Learning to Lie for Node Classification Taskscited by 0
  30. 2024SES: Bridging the Gap Between Explainability and Prediction of Graph Neural Networkscited by 0
  31. 2024Graph Structure Prompt Learning: A Novel Methodology to Improve Performance of Graph Neural Networkscited by 0
  32. 2024Information propagation dynamics in Deep Graph Networkscited by 0
  33. 2025Tensor Convolutional Network for Higher-Order Interaction Prediction in Sparse Tensorscited by 0
  34. 2025TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flowscited by 0
  35. 2025Non-Dissipative Graph Propagation for Non-Local Community Detectioncited by 0
  36. 2025Graph Neural Networks with Transformer Fusion of Brain Connectivity Dynamics and Tabular Data for Forecasting Future Tobacco Usecited by 0
  37. 2026Geometry-Induced Diffusion on Graphs: A Learnable Weighted Laplacian for Spectral GNNscited by 0
  38. 2026Graph Hierarchical Recurrence for Long-Range Generalizationcited by 0

50 most cited of 58 All 58 (JSON)