# Learnable Filters for Geometric Scattering Modules

arXiv: https://arxiv.org/abs/2208.07458 · HTML: https://mlsanity.com/paper/2208.07458/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 54 references that are in the map.
- First posted on arXiv 15 Aug 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1906.02174/) (2019)
- [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)
- [Diffusion Scattering Transforms on Graphs](https://mlsanity.com/paper/1806.08829/) (2018)
- [Stability of Graph Scattering Transforms](https://mlsanity.com/paper/1906.04784/) (2019)
- [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)
- [Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms](https://mlsanity.com/paper/1911.06253/) (2019)
- [The Manifold Scattering Transform for High-Dimensional Point Cloud Data](https://mlsanity.com/paper/2206.10078/) (2022)
- [Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds](https://mlsanity.com/paper/1905.10448/) (2019)

## Built on by (most cited first, 9 of 9)

- [Hyperedge Representations with Hypergraph Wavelets: Applications to Spatial Transcriptomics](https://mlsanity.com/paper/2409.09469/) (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)
- [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)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [Interpetable Target-Feature Aggregation for Multi-Task Learning based on Bias-Variance Analysis](https://mlsanity.com/paper/2406.07991/) (2024)
- [InfoGain Wavelets: Furthering the Design of Graph Diffusion Wavelets](https://mlsanity.com/paper/2504.08802/) (2025)
- [SlepNet: Spectral Subgraph Representation Learning for Neural Dynamics](https://mlsanity.com/paper/2506.16602/) (2025)

## Abstract (arXiv)

We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks. Our results show that LEGS-based networks match or outperforms popular GNNs, as well as the original geometric scattering construction, on many datasets, in particular in biochemical domains, while retaining certain mathematical properties of handcrafted (non-learned) geometric scattering.