mlsanityData to 7 Oct 2026

VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks

arXiv 2510.01022 ↗First posted 1 Oct 2025cs.LG eess.SP stat.MLcited by 1

Not on the map. Why?

Abstract (arXiv)

We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets may be effectively incorporated into a family of geometric graph neural networks, which we refer to as VDW-GNNs. We demonstrate that such networks are effective on synthetic point cloud data, as well as on real-world data derived from wind field and neural activity measurements. Theoretically, we prove that these new wavelets have desirable frame theoretic properties, similar to traditional diffusion wavelets. Additionally, we prove that these wavelets have useful symmetries with respect to rotations and translations.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 58 of its 88 references that are in the map. First posted on arXiv 1 Oct 2025.

Builds on

58 of 88 references.

References · 58

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2020Supervised Contrastive Learningcited by 2,803
  6. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  7. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  8. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  9. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  10. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  11. 2021E(n) Equivariant Graph Neural Networkscited by 951
  12. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
38 more
  1. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  4. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 409
  5. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  6. 2022Learnable latent embeddings for joint behavioral and neural analysiscited by 113
  7. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  8. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  9. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  10. 2018Kymatio: Scattering Transforms in Pythoncited by 54
  11. 2018Geometric Scattering for Graph Data Analysiscited by 49
  12. 2015A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extractioncited by 46
  13. 2018Graph Convolutional Neural Networks via Scatteringcited by 46
  14. 2018Diffusion Scattering Transforms on Graphscited by 43
  15. 2017Scaling the Scattering Transform: Deep Hybrid Networkscited by 35
  16. 2022Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?cited by 25
  17. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 21
  18. 2013Spectral Convergence of the connection Laplacian from random samplescited by 19
  19. 2022Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networkscited by 18
  20. 2022Geometric Scattering on Measure Spacescited by 17
  21. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 13
  22. 2018Solid Harmonic Wavelet Scattering for Predictions of Molecule Propertiescited by 12
  23. 2023Interpretable statistical representations of neural population dynamics and geometrycited by 12
  24. 2023NodeMixup: Tackling Under-Reaching for Graph Neural Networkscited by 12
  25. 2019Understanding Graph Neural Networks with Generalized Geometric Scattering Transformscited by 11
  26. 2024On the Completeness of Invariant Geometric Deep Learning Modelscited by 11
  27. 2021Stability of Neural Networks on Manifolds to Relative Perturbationscited by 9
  28. 2022The Manifold Scattering Transform for High-Dimensional Point Cloud Datacited by 9
  29. 2022Learnable Filters for Geometric Scattering Modulescited by 9
  30. 2024Towards a General Recipe for Combinatorial Optimization with Multi-Filter GNNscited by 9
  31. 2021Stability to Deformations of Manifold Filters and Manifold Neural Networkscited by 8
  32. 2019Geometric Wavelet Scattering Networks on Compact Riemannian Manifoldscited by 7
  33. 2021Molecular Graph Generation via Geometric Scatteringcited by 7
  34. 2015Deep Convolutional Neural Networks Based on Semi-Discrete Framescited by 6
  35. 2022A Convergence Rate for Manifold Neural Networkscited by 6
  36. 2024Generalization of Geometric Graph Neural Networks with Lipschitz Loss Functionscited by 6
  37. 2020Geometric Scattering Attention Networkscited by 5
  38. 2022Multiscale Transforms for Signals on Simplicial Complexescited by 4

50 most cited of 58 All 58 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Transversal Pooling Neural Networkscited by 0