# Graph Scattering beyond Wavelet Shackles

arXiv: https://arxiv.org/abs/2301.11456 · HTML: https://mlsanity.com/paper/2301.11456/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [N-Gram Graph: Simple Unsupervised Representation for Graphs, with Applications to Molecules](https://mlsanity.com/paper/1806.09206/) (2018)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks](https://mlsanity.com/paper/2003.08414/) (2020)
- [Geometric Scattering for Graph Data Analysis](https://mlsanity.com/paper/1810.03068/) (2018)
- [A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction](https://mlsanity.com/paper/1512.06293/) (2015)
- [Graph Convolutional Neural Networks via Scattering](https://mlsanity.com/paper/1804.00099/) (2018)
- [Diffusion Scattering Transforms on Graphs](https://mlsanity.com/paper/1806.08829/) (2018)
- [Stability of Graph Scattering Transforms](https://mlsanity.com/paper/1906.04784/) (2019)
- [Path-Augmented Graph Transformer Network](https://mlsanity.com/paper/1905.12712/) (2019)
- [Deep Molecular Representation Learning via Fusing Physical and Chemical Information](https://mlsanity.com/paper/2112.04624/) (2021)
- [Spatio-Temporal Graph Scattering Transform](https://mlsanity.com/paper/2012.03363/) (2020)
- [Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames](https://mlsanity.com/paper/1311.0897/) (2013)
- [Learning Hyperbolic Representations of Topological Features](https://mlsanity.com/paper/2103.09273/) (2021)

## Built on by (most cited first, 2 of 2)

- [HoloNets: Spectral Convolutions do extend to Directed Graphs](https://mlsanity.com/paper/2310.02232/) (2023)
- [A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition](https://mlsanity.com/paper/2405.13806/) (2024)

## Abstract (arXiv)

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for node- and graph-level perturbations are derived; the vertex-set non-preserving case is treated by utilizing recently developed mathematical-physics based tools. Energy propagation through the network layers is investigated and related to truncation stability. New methods of graph-level feature aggregation are introduced and stability of the resulting composite scattering architectures is established. Finally, scattering transforms are extended to edge- and higher order tensorial input. Theoretical results are complemented by numerical investigations: Suitably chosen cattering networks conforming to the developed theory perform better than traditional graph-wavelet based scattering approaches in social network graph classification tasks and significantly outperform other graph-based learning approaches to regression of quantum-chemical energies on QM7.