mlsanityData to 14 Oct 2026

ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks

arXiv 2206.05437 ↗First posted 11 Jun 2022cs.LG cs.AI math.APcited by 31

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Abstract (arXiv)

Neural message passing is a basic feature extraction unit for graph-structured data considering neighboring node features in network propagation from one layer to the next. We model such process by an interacting particle system with attractive and repulsive forces and the Allen-Cahn force arising in the modeling of phase transition. The dynamics of the system is a reaction-diffusion process which can separate particles without blowing up. This induces an Allen-Cahn message passing (ACMP) for graph neural networks where the numerical iteration for the particle system solution constitutes the message passing propagation. ACMP which has a simple implementation with a neural ODE solver can propel the network depth up to one hundred of layers with theoretically proven strictly positive lower bound of the Dirichlet energy. It thus provides a deep model of GNNs circumventing the common GNN problem of oversmoothing. GNNs with ACMP achieve state of the art performance for real-world node classification tasks on both homophilic and heterophilic datasets. Codes are available at https://github.com/ykiiiiii/ACMP.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 37 of its 63 references that are in the map. First posted on arXiv 11 Jun 2022.

Builds on

37 of 63 references.

References · 37

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Inductive Representation Learning on Large Graphscited by 6,320
  4. 2018How Powerful are Graph Neural Networks?cited by 4,393
  5. 2018Neural Ordinary Differential Equationscited by 3,779
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  7. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
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  11. 2018Pitfalls of Graph Neural Network Evaluationcited by 1,007
  12. 2020Simple and Deep Graph Convolutional Networkscited by 860
25 more
  1. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  2. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  3. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  4. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  5. 2019Diffusion Improves Graph Learningcited by 414
  6. 2022Message Passing Neural PDE Solverscited by 386
  7. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 311
  8. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  9. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 261
  10. 2021GRAND: Graph Neural Diffusioncited by 258
  11. 2020A Note on Over-Smoothing for Graph Neural Networkscited by 249
  12. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  13. 2017Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equationscited by 203
  14. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  15. 2019Graph Neural Ordinary Differential Equationscited by 154
  16. 2022Graph-Coupled Oscillator Networkscited by 124
  17. 2019Continuous Graph Neural Networkscited by 114
  18. 2021Geometric Deep Learning on Molecular Representationscited by 113
  19. 2019Hamiltonian Graph Networks with ODE Integratorscited by 108
  20. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  21. 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
  22. 2020On Second Order Behaviour in Augmented Neural ODEscited by 68
  23. 2019Fast and Deep Graph Neural Networkscited by 35
  24. 2017A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part Icited by 15
  25. 2019Discrete and Continuous Deep Residual Learning Over Graphscited by 13

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 8; 2024: 9; 2025: 8; 2026: 4.

31 papers.

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  1. 2023DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusioncited by 87
  2. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  3. 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
  4. 2023Graph Neural Convection-Diffusion with Heterophilycited by 26
  5. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  6. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 17
  7. 2024Understanding Oversmoothing in Diffusion-Based GNNs From the Perspective of Operator Semigroup Theorycited by 8
  8. 2024Distributed-Order Fractional Graph Operating Networkcited by 7
  9. 2023From Cluster Assumption to Graph Convolution: Graph-based Semi-Supervised Learning Revisitedcited by 6
  10. 2024Design Your Own Universe: A Physics-Informed Agnostic Method for Enhancing Graph Neural Networkscited by 6
  11. 2025Are We Measuring Oversmoothing in Graph Neural Networks Correctly?cited by 6
  12. 2024Oversmoothing Alleviation in Graph Neural Networks: A Survey and Unified Viewcited by 4
19 more
  1. 2022Domain-informed graph neural networks: a quantum chemistry case studycited by 3
  2. 2024Foundations and Frontiers of Graph Learning Theorycited by 3
  3. 2024When Graph Neural Networks Meet Dynamic Mode Decompositioncited by 3
  4. 2024Improving Graph Neural Networks by Learning Continuous Edge Directionscited by 3
  5. 2025A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNscited by 2
  6. 2025Early-Exit Graph Neural Networkscited by 2
  7. 2026Beyond ReLU: Bifurcation, Oversmoothing, and Topological Priorscited by 2
  8. 2023A Unified View on Neural Message Passing with Opinion Dynamics for Social Networkscited by 1
  9. 2023Graph Neural Networks with a Distribution of Parametrized Graphscited by 1
  10. 2025TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flowscited by 1
  11. 2025Graph Neural Regularizers for PDE Inverse Problemscited by 1
  12. 2025Measuring Over-smoothing beyond Dirichlet energycited by 1
  13. 2026Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learningcited by 1
  14. 2023DFGET: Displacement-Field Assisted Graph Energy Transmitter for Gland Instance Segmentationcited by 0
  15. 2024Message Detouring: A Simple Yet Effective Cycle Representation for Expressive Graph Learningcited by 0
  16. 2025Heterophily-informed Message Passingcited by 0
  17. 2025How Particle System Theory Enhances Hypergraph Message Passingcited by 0
  18. 2026Modeling Whole-Slide Images as Dynamic Tumor Microenvironment Fieldscited by 0
  19. 2026Propagate, Then Sharpen: Post-Hoc Refinement of Frozen Node Classifierscited by 0