mlsanityData to 7 Oct 2026

Diffusion Scattering Transforms on Graphs

arXiv 1806.08829 ↗First posted 22 Jun 2018cs.LG stat.MLcited by 43

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Abstract (arXiv)

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture "high-frequency" information, akin to the Euclidean Scattering.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 12; 2023: 10; 2024: 5; 2025: 6; 2026: 3.

43 papers.

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  1. 2022Rethinking Graph Neural Networks for Anomaly Detectioncited by 185
  2. 2022Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networkscited by 94
  3. 2022Unlearning Graph Classifiers with Limited Data Resourcescited by 31
  4. 2022Skeleton-Parted Graph Scattering Networks for 3D Human Motion Predictioncited by 29
  5. 2022Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?cited by 25
  6. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  7. 2021Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNscited by 18
  8. 2021Stability of Graph Convolutional Neural Networks to Stochastic Perturbationscited by 18
  9. 2022Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networkscited by 18
  10. 2022Geometric Scattering on Measure Spacescited by 17
  11. 2023Approximately Equivariant Graph Networkscited by 16
  12. 2023A Survey of Graph Unlearningcited by 12
31 more
  1. 2021Adaptive Gaussian Processes on Graphs via Spectral Graph Waveletscited by 11
  2. 2022From Local to Global: Spectral-Inspired Graph Neural Networkscited by 11
  3. 2022The Manifold Scattering Transform for High-Dimensional Point Cloud Datacited by 9
  4. 2022Learnable Filters for Geometric Scattering Modulescited by 9
  5. 2021Convolutional Filtering and Neural Networks with Non Commutative Algebrascited by 8
  6. 2021Molecular Graph Generation via Geometric Scatteringcited by 7
  7. 2021Graph Neural Networks With Lifting-based Adaptive Graph Waveletscited by 6
  8. 2024A General Graph Spectral Wavelet Convolution via Chebyshev Order Decompositioncited by 4
  9. 2023Contrastive Learning for Non-Local Graphs with Multi-Resolution Structural Viewscited by 3
  10. 2023DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveformscited by 3
  11. 2023BLIS-Net: Classifying and Analyzing Signals on Graphscited by 3
  12. 2023Graph Scattering beyond Wavelet Shacklescited by 2
  13. 2023Manifold Filter-Combine Networkscited by 2
  14. 2023Directed Scattering for Knowledge Graph-based Cellular Signaling Analysiscited by 2
  15. 2023On the Trade-Off between Stability and Representational Capacity in Graph Neural Networkscited by 2
  16. 2025HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Datacited by 2
  17. 2025WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generationcited by 2
  18. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  19. 2021Spatio-Temporal Graph Complementary Scattering Networkscited by 0
  20. 2022Tuning the Geometry of Graph Neural Networkscited by 0
  21. 2023ViDa: Visualizing DNA hybridization trajectories with biophysics-informed deep graph embeddingscited by 0
  22. 2024A short review on the maximum clique problem algorithms with classical, AI, and quantum methodscited by 0
  23. 2024Convergence of Manifold Filter-Combine Networkscited by 0
  24. 2024ProtScape: A molecular structure and energy-aware representation for protein conformation generationcited by 0
  25. 2024GeoScatt-GNN: A Geometric Scattering Transform-Based Graph Neural Network Model for Ames Mutagenicity Predictioncited by 0
  26. 2025InfoGain Wavelets: Furthering the Design of Graph Diffusion Waveletscited by 0
  27. 2025Convexified Message-Passing Graph Neural Networkscited by 0
  28. 2025ARM-Explainer -- Explaining and improving graph neural network predictions for the maximum clique problem using node features and association rule miningcited by 0
  29. 2026Data-Driven Graph Filters via Adaptive Spectral Shapingcited by 0
  30. 2026Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?cited by 0
  31. 2026Transversal Pooling Neural Networkscited by 0