mlsanityData to 7 Oct 2026

Stability of Graph Scattering Transforms

arXiv 1906.04784 ↗First posted 11 Jun 2019cs.LG stat.MLcited by 34

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Abstract (arXiv)

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stability property dons the scattering transform with a robustness to small changes in the metric domain of the data. When considering network data, regular convolutions do not hold since the data domain presents an irregular structure given by the network topology. In this work, we extend scattering transforms to network data by using multiresolution graph wavelets, whose computation can be obtained by means of graph convolutions. Furthermore, we prove that the resulting graph scattering transforms are stable to metric perturbations of the underlying network. This renders graph scattering transforms robust to changes on the network topology, making it particularly useful for cases of transfer learning, topology estimation or time-varying graphs.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jun 2019.

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Citing papers per year: 2021: 8; 2022: 11; 2023: 7; 2024: 3; 2025: 5.

34 papers.

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  1. 2022Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networkscited by 94
  2. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  3. 2022Certified Graph Unlearningcited by 46
  4. 2021Transferability Properties of Graph Neural Networkscited by 42
  5. 2022Unlearning Graph Classifiers with Limited Data Resourcescited by 31
  6. 2022Skeleton-Parted Graph Scattering Networks for 3D Human Motion Predictioncited by 29
  7. 2023Convolutional Learning on Simplicial Complexescited by 26
  8. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  9. 2021Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNscited by 18
  10. 2022Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networkscited by 18
  11. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 13
  12. 2021Space-Time Graph Neural Networkscited by 10
22 more
  1. 2021Stability of Neural Networks on Manifolds to Relative Perturbationscited by 9
  2. 2022The Manifold Scattering Transform for High-Dimensional Point Cloud Datacited by 9
  3. 2022Learnable Filters for Geometric Scattering Modulescited by 9
  4. 2021Stability to Deformations of Manifold Filters and Manifold Neural Networkscited by 8
  5. 2021Molecular Graph Generation via Geometric Scatteringcited by 7
  6. 2021Graph Neural Networks With Lifting-based Adaptive Graph Waveletscited by 6
  7. 2023Stochastic Unrolled Federated Learningcited by 6
  8. 2021On the Stability of Low Pass Graph Filter With a Large Number of Edge Rewirescited by 5
  9. 2024A General Graph Spectral Wavelet Convolution via Chebyshev Order Decompositioncited by 4
  10. 2023DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveformscited by 3
  11. 2023BLIS-Net: Classifying and Analyzing Signals on Graphscited by 3
  12. 2022On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networkscited by 2
  13. 2023Graph Scattering beyond Wavelet Shacklescited by 2
  14. 2023Manifold Filter-Combine Networkscited by 2
  15. 2025HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Datacited by 2
  16. 2023Multiscale Hodge Scattering Networks for Data Analysiscited by 1
  17. 2024MS-IMAP -- A Multi-Scale Graph Embedding Approach for Interpretable Manifold Learningcited by 1
  18. 2025Covariance Scattering Transformscited by 1
  19. 2024Convergence of Manifold Filter-Combine Networkscited by 0
  20. 2025InfoGain Wavelets: Furthering the Design of Graph Diffusion Waveletscited by 0
  21. 2025Convexified Message-Passing Graph Neural Networkscited by 0
  22. 2025Graph Semi-Supervised Learning for Point Classification on Data Manifoldscited by 0