# Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

arXiv: https://arxiv.org/abs/1905.10448 · HTML: https://mlsanity.com/paper/1905.10448/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 7 of 7)

- [Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs](https://mlsanity.com/paper/2102.02828/) (2021)
- [Parametric Scattering Networks](https://mlsanity.com/paper/2107.09539/) (2021)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)
- [On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networks](https://mlsanity.com/paper/2209.11740/) (2022)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [Scattering Networks on Noncommutative Finite Groups](https://mlsanity.com/paper/2505.20950/) (2025)
- [Transversal Pooling Neural Networks](https://mlsanity.com/paper/2609.36237/) (2026)

## Abstract (arXiv)

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.