# Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

arXiv: https://arxiv.org/abs/1911.06253 · HTML: https://mlsanity.com/paper/1911.06253/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2019.

## Built on by (most cited first, 12 of 12)

- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)
- [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)
- [HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data](https://mlsanity.com/paper/2502.07746/) (2025)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [Graph Neural Networks Are Not Continuous Across Graph Resolutions](https://mlsanity.com/paper/2605.31315/) (2026)
- [ProtScape: A molecular structure and energy-aware representation for protein conformation generation](https://mlsanity.com/paper/2410.20317/) (2024)
- [Digital implementations of deep feature extractors are intrinsically informative](https://mlsanity.com/paper/2502.15004/) (2025)
- [InfoGain Wavelets: Furthering the Design of Graph Diffusion Wavelets](https://mlsanity.com/paper/2504.08802/) (2025)
- [Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs](https://mlsanity.com/paper/2602.10031/) (2026)
- [Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?](https://mlsanity.com/paper/2603.02462/) (2026)
- [Cone Rayleigh Levels: Finite Perturbations and Certified Control](https://mlsanity.com/paper/2608.27122/) (2026)

## Abstract (arXiv)

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducing windowed and non-windowed geometric scattering transforms for graphs based upon a very general class of asymmetric wavelets. We show that these asymmetric graph scattering transforms have many of the same theoretical guarantees as their symmetric counterparts. As a result, the proposed construction unifies and extends known theoretical results for many of the existing graph scattering architectures. In doing so, this work helps bridge the gap between geometric scattering and other graph neural networks by introducing a large family of networks with provable stability and invariance guarantees. These results lay the groundwork for future deep learning architectures for graph-structured data that have learned filters and also provably have desirable theoretical properties.