mlsanityData to 13 Oct 2026

GREAD: Graph Neural Reaction-Diffusion Networks

arXiv 2211.14208 ↗First posted 25 Nov 2022cs.LGcited by 54

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Abstract (arXiv)

Graph neural networks (GNNs) are one of the most popular research topics for deep learning. GNN methods typically have been designed on top of the graph signal processing theory. In particular, diffusion equations have been widely used for designing the core processing layer of GNNs, and therefore they are inevitably vulnerable to the notorious oversmoothing problem. Recently, a couple of papers paid attention to reaction equations in conjunctions with diffusion equations. However, they all consider limited forms of reaction equations. To this end, we present a reaction-diffusion equation-based GNN method that considers all popular types of reaction equations in addition to one special reaction equation designed by us. To our knowledge, our paper is one of the most comprehensive studies on reaction-diffusion equation-based GNNs. In our experiments with 9 datasets and 28 baselines, our method, called GREAD, outperforms them in a majority of cases. Further synthetic data experiments show that it mitigates the oversmoothing problem and works well for various homophily rates.

Key facts. Cited by 54 papers in the map (data through 13 Oct 2026). Builds on 45 of its 74 references that are in the map. First posted on arXiv 25 Nov 2022.

Builds on

45 of 74 references.

References · 45

  1. 2017Attention Is All You Needcited by 60,106
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,318
  3. 2017Graph Attention Networkscited by 8,888
  4. 2017Inductive Representation Learning on Large Graphscited by 6,303
  5. 2018Neural Ordinary Differential Equationscited by 3,750
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,471
  7. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,086
  8. 2019Simplifying Graph Convolutional Networkscited by 1,474
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  11. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 973
  12. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 877
33 more
  1. 2020Simple and Deep Graph Convolutional Networkscited by 857
  2. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  3. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  4. 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 583
  5. 2019Multi-scale Attributed Node Embeddingcited by 546
  6. 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
  7. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  8. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 443
  9. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 362
  10. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 311
  11. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  12. 2020Towards Deeper Graph Neural Networkscited by 296
  13. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 261
  14. 2021GRAND: Graph Neural Diffusioncited by 258
  15. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 210
  16. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  17. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  18. 2018Adaptive Sampling Towards Fast Graph Representation Learningcited by 180
  19. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  20. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  21. 2019Graph Neural Ordinary Differential Equationscited by 154
  22. 2018Contextual Stochastic Block Modelscited by 134
  23. 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
  24. 2022Graph-Coupled Oscillator Networkscited by 124
  25. 2019Continuous Graph Neural Networkscited by 114
  26. 2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
  27. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  28. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  29. 2022Blurring-Sharpening Process Models for Collaborative Filteringcited by 35
  30. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  31. 2021LT-OCF: Learnable-Time ODE-based Collaborative Filteringcited by 21
  32. 2021Climate Modeling with Neural Diffusion Equationscited by 20
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Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 8; 2024: 16; 2025: 22; 2026: 8.

54 papers.

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  1. 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
  2. 2023An Attentive Inductive Bias for Sequential Recommendation beyond the Self-Attentioncited by 28
  3. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 28
  4. 2024Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systemscited by 25
  5. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  6. 2023Graph Neural Rough Differential Equations for Traffic Forecastingcited by 14
  7. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  8. 2023Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyondcited by 13
  9. 2023Graph Convolutions Enrich the Self-Attention in Transformers!cited by 11
  10. 2024Temporal Graph ODEs for Irregularly-Sampled Time Seriescited by 11
  11. 2025Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modelingcited by 10
  12. 2026Learning Posterior Predictive Distributions for Node Classification from Synthetic Graph Priorscited by 10
38 more
  1. 2024Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Studycited by 9
  2. 2024On The Temporal Domain of Differential Equation Inspired Graph Neural Networkscited by 9
  3. 2025Can TabPFN Compete with GNNs for Node Classification via Graph Tabularization?cited by 9
  4. 2024Understanding Oversmoothing in Diffusion-Based GNNs From the Perspective of Operator Semigroup Theorycited by 8
  5. 2023Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftingscited by 6
  6. 2025Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Modelscited by 6
  7. 2024SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classificationcited by 4
  8. 2024DeepSN: A Sheaf Neural Framework for Influence Maximizationcited by 4
  9. 2023RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendationcited by 3
  10. 2024When Graph Neural Networks Meet Dynamic Mode Decompositioncited by 3
  11. 2025Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learningcited by 3
  12. 2025Stuart-Landau Oscillatory Graph Neural Networkcited by 3
  13. 2025Are Graph Transformers Necessary? Efficient Long-Range Message Passing with Fractal Nodes in MPNNscited by 3
  14. 2023Improving Signed Propagation for Graph Neural Networks in Multi-Class Environmentscited by 2
  15. 2024Graph Neural Aggregation-diffusion with Metastabilitycited by 2
  16. 2024Quadratic Binary Optimization with Graph Neural Networkscited by 2
  17. 2024Faster Local Solvers for Graph Diffusion Equationscited by 2
  18. 2025Resolving Oversmoothing with Opinion Dissensuscited by 2
  19. 2024Link Prediction with Physics-Inspired Graph Neural Networkscited by 1
  20. 2025Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fieldscited by 1
  21. 2025TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flowscited by 1
  22. 2025Wavy Transformercited by 1
  23. 2025A Causality-Aware Spatiotemporal Model for Multi-Region and Multi-Pollutant Air Quality Forecastingcited by 1
  24. 2025On the Convergence and Size Transferability of Continuous-depth Graph Neural Networkscited by 1
  25. 2025Graph Neural Regularizers for PDE Inverse Problemscited by 1
  26. 2025Measuring Over-smoothing beyond Dirichlet energycited by 1
  27. 2024HoGA: Higher-Order Graph Attention via Diversity-Aware k-Hop Samplingcited by 0
  28. 2024Graph Spring Neural ODEs for Link Sign Predictioncited by 0
  29. 2025Non-Dissipative Graph Propagation for Non-Local Community Detectioncited by 0
  30. 2025Spatiotemporal graph neural process for reconstruction, extrapolation, and classification of cardiac trajectoriescited by 0
  31. 2025Structure-Attribute Transformations with Markov Chain Boost Graph Domain Adaptationcited by 0
  32. 2025An Active Diffusion Neural Network for Graphscited by 0
  33. 2025Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  34. 2025Complex-Weighted Convolutional Networks: Provable Expressiveness via Complex Diffusioncited by 0
  35. 2025Rethinking Message Passing Neural Networks with Diffusion Distance-guided Stress Majorizationcited by 0
  36. 2026Lyapunov Stable Graph Neural Flowcited by 0
  37. 2026Graph Navier Stokes Networkscited by 0
  38. 2026From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networkscited by 0

50 most cited of 54 All 54 (JSON)