# Stability of Graph Scattering Transforms

arXiv: https://arxiv.org/abs/1906.04784 · HTML: https://mlsanity.com/paper/1906.04784/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2019.

## Built on by (most cited first, 30 of 34)

- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Certified Graph Unlearning](https://mlsanity.com/paper/2206.09140/) (2022)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [Unlearning Graph Classifiers with Limited Data Resources](https://mlsanity.com/paper/2211.03216/) (2022)
- [Skeleton-Parted Graph Scattering Networks for 3D Human Motion Prediction](https://mlsanity.com/paper/2208.00368/) (2022)
- [Convolutional Learning on Simplicial Complexes](https://mlsanity.com/paper/2301.11163/) (2023)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs](https://mlsanity.com/paper/2102.02828/) (2021)
- [Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks](https://mlsanity.com/paper/2201.08932/) (2022)
- [Convolutional Neural Networks on Manifolds: From Graphs and Back](https://mlsanity.com/paper/2210.00376/) (2022)
- [Space-Time Graph Neural Networks](https://mlsanity.com/paper/2110.02880/) (2021)
- [Stability to Deformations of Manifold Filters and Manifold Neural Networks](https://mlsanity.com/paper/2106.03725/) (2021)
- [Stability of Neural Networks on Manifolds to Relative Perturbations](https://mlsanity.com/paper/2110.04702/) (2021)
- [The Manifold Scattering Transform for High-Dimensional Point Cloud Data](https://mlsanity.com/paper/2206.10078/) (2022)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)
- [Molecular Graph Generation via Geometric Scattering](https://mlsanity.com/paper/2110.06241/) (2021)
- [Graph Neural Networks With Lifting-based Adaptive Graph Wavelets](https://mlsanity.com/paper/2108.01660/) (2021)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [On the Stability of Low Pass Graph Filter With a Large Number of Edge Rewires](https://mlsanity.com/paper/2110.07234/) (2021)
- [A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition](https://mlsanity.com/paper/2405.13806/) (2024)
- [DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms](https://mlsanity.com/paper/2309.09924/) (2023)
- [BLIS-Net: Classifying and Analyzing Signals on Graphs](https://mlsanity.com/paper/2310.17579/) (2023)
- [On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networks](https://mlsanity.com/paper/2209.11740/) (2022)
- [Graph Scattering beyond Wavelet Shackles](https://mlsanity.com/paper/2301.11456/) (2023)
- [Manifold Filter-Combine Networks](https://mlsanity.com/paper/2307.04056/) (2023)
- [HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data](https://mlsanity.com/paper/2502.07746/) (2025)
- [Covariance Scattering Transforms](https://mlsanity.com/paper/2511.08878/) (2025)
- [Multiscale Hodge Scattering Networks for Data Analysis](https://mlsanity.com/paper/2311.10270/) (2023)
- [MS-IMAP -- A Multi-Scale Graph Embedding Approach for Interpretable Manifold Learning](https://mlsanity.com/paper/2406.02778/) (2024)

## 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.