mlsanityData to 14 Oct 2026

Generalized energy and gradient flow via graph framelets

arXiv 2210.04124 ↗First posted 8 Oct 2022cs.LG stat.MLcited by 10

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Abstract (arXiv)

In this work, we provide a theoretical understanding of the framelet-based graph neural networks through the perspective of energy gradient flow. By viewing the framelet-based models as discretized gradient flows of some energy, we show it can induce both low-frequency and high-frequency-dominated dynamics, via the separate weight matrices for different frequency components. This substantiates its good empirical performance on both homophilic and heterophilic graphs. We then propose a generalized energy via framelet decomposition and show its gradient flow leads to a novel graph neural network, which includes many existing models as special cases. We then explain how the proposed model generally leads to more flexible dynamics, thus potentially enhancing the representation power of graph neural networks.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 47 of its 58 references that are in the map. First posted on arXiv 8 Oct 2022.

Builds on

47 of 58 references.

References · 47

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Graph Attention Networkscited by 8,923
  4. 2017Inductive Representation Learning on Large Graphscited by 6,320
  5. 2018How Powerful are Graph Neural Networks?cited by 4,393
  6. 2018Neural Ordinary Differential Equationscited by 3,779
  7. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  8. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  9. 2019Simplifying Graph Convolutional Networkscited by 1,477
  10. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  11. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 993
  12. 2020Simple and Deep Graph Convolutional Networkscited by 860
35 more
  1. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  2. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 754
  3. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  4. 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 584
  5. 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
  6. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 478
  7. 2019Diffusion Improves Graph Learningcited by 414
  8. 2019Provably Powerful Graph Networkscited by 389
  9. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 362
  10. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 261
  11. 2021GRAND: Graph Neural Diffusioncited by 258
  12. 2020A Note on Over-Smoothing for Graph Neural Networkscited by 249
  13. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  14. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  15. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  16. 2019Graph Neural Ordinary Differential Equationscited by 154
  17. 2018Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecastingcited by 146
  18. 2019Graph Wavelet Neural Networkcited by 131
  19. 2022Graph-Coupled Oscillator Networkscited by 124
  20. 2019Continuous Graph Neural Networkscited by 114
  21. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  22. 2020Sheaf Neural Networkscited by 84
  23. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  24. 2019Community Detection on Networks with Ricci Flowcited by 62
  25. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  26. 2021How Framelets Enhance Graph Neural Networkscited by 46
  27. 2022Optimization-Induced Graph Implicit Nonlinear Diffusioncited by 28
  28. 2019Fast Haar Transforms for Graph Neural Networkscited by 20
  29. 2020Decimated Framelet System on Graphs and Fast G-Framelet Transformscited by 17
  30. 2019Discrete and Continuous Deep Residual Learning Over Graphscited by 13
  31. 2018Exploring Weight Symmetry in Deep Neural Networkscited by 12
  32. 2021Graph Denoising with Framelet Regularizercited by 8
  33. 2022A Simple Yet Effective SVD-GCN for Directed Graphscited by 7
  34. 2021A Deep Graph Wavelet Convolutional Neural Network for Semi-supervised Node Classificationcited by 4
  35. 2021Spectral Transform Forms Scalable Transformercited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 6; 2024: 2; 2025: 0; 2026: 1.

10 papers.

  1. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  2. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  3. 2023How Curvature Enhance the Adaptation Power of Framelet GCNscited by 13
  4. 2023Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyondcited by 13
  5. 2024Design Your Own Universe: A Physics-Informed Agnostic Method for Enhancing Graph Neural Networkscited by 6
  6. 2026Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equationscited by 5
  7. 2024When Graph Neural Networks Meet Dynamic Mode Decompositioncited by 3
  8. 2023Frameless Graph Knowledge Distillationcited by 2
  9. 2023Revisiting Generalized p-Laplacian Regularized Framelet GCNs: Convergence, Energy Dynamic and Training with Non-Linear Diffusioncited by 1
  10. 2022Generalized Laplacian Regularized Framelet Graph Neural Networkscited by 0