# Multiscale Hodge Scattering Networks for Data Analysis

arXiv: https://arxiv.org/abs/2311.10270 · HTML: https://mlsanity.com/paper/2311.10270/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 65 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [word2vec Parameter Learning Explained](https://mlsanity.com/paper/1411.2738/) (2014)
- [Geometric Scattering for Graph Data Analysis](https://mlsanity.com/paper/1810.03068/) (2018)
- [Graph Convolutional Neural Networks via Scattering](https://mlsanity.com/paper/1804.00099/) (2018)
- [Universal Graph Transformer Self-Attention Networks](https://mlsanity.com/paper/1909.11855/) (2019)
- [Are Powerful Graph Neural Nets Necessary? A Dissection on Graph Classification](https://mlsanity.com/paper/1905.04579/) (2019)
- [Stability of Graph Scattering Transforms](https://mlsanity.com/paper/1906.04784/) (2019)
- [Signal Processing on Cell Complexes](https://mlsanity.com/paper/2110.05614/) (2021)
- [SchNetPack 2.0: A neural network toolbox for atomistic machine learning](https://mlsanity.com/paper/2212.05517/) (2022)
- [Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data](https://mlsanity.com/paper/1601.01704/) (2016)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [Hodgelets: Localized Spectral Representations of Flows on Simplicial Complexes](https://mlsanity.com/paper/2109.08728/) (2021)
- [Topological Slepians: Maximally Localized Representations of Signals over Simplicial Complexes](https://mlsanity.com/paper/2210.14758/) (2022)
- [Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud data](https://mlsanity.com/paper/2103.07626/) (2021)
- [Deep Haar Scattering Networks](https://mlsanity.com/paper/1509.09187/) (2015)
- [Multiscale Transforms for Signals on Simplicial Complexes](https://mlsanity.com/paper/2301.02136/) (2022)
- [Monogenic Wavelet Scattering Network for Texture Image Classification](https://mlsanity.com/paper/2202.12491/) (2022)

## Built on by (most cited first, 1 of 1)

- [HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data](https://mlsanity.com/paper/2502.07746/) (2025)

## Abstract (arXiv)

We propose new scattering networks for signals measured on simplicial complexes, which we call Multiscale Hodge Scattering Networks (MHSNs). Our construction builds on multiscale basis dictionaries on simplicial complexes -- namely, the kappa-GHWT and kappa-HGLET -- which we recently developed for simplices of dimension kappa ∈ mathbbN in a given simplicial complex by generalizing the node-based Generalized Haar--Walsh Transform (GHWT) and Hierarchical Graph Laplacian Eigen Transform (HGLET). Both the kappa-GHWT and the kappa-HGLET form redundant sets (i.e., dictionaries) of multiscale basis vectors and the corresponding expansion coefficients of a given signal. Our MHSNs adopt a layered structure analogous to a convolutional neural network (CNN), cascading the moments of the modulus of the dictionary coefficients. The resulting features are invariant to reordering of the simplices (i.e., node permutation of the underlying graphs). Importantly, the use of multiscale basis dictionaries in our MHSNs admits a natural pooling operation -- akin to local pooling in CNNs -- that can be performed either locally or per scale. Such pooling operations are more difficult to define in traditional scattering networks based on Morlet wavelets and in geometric scattering networks based on Diffusion Wavelets. As a result, our approach extracts a rich set of descriptive yet robust features that can be combined with simple machine learning models (e.g., logistic regression or support vector machines) to achieve high-accuracy classification with far fewer trainable parameters than most modern graph neural networks require. Finally, we demonstrate the effectiveness of MHSNs on three distinct problem types: signal classification, domain (i.e., graph/simplex) classification, and molecular dynamics prediction.