# InfoGain Wavelets: Furthering the Design of Graph Diffusion Wavelets

arXiv: https://arxiv.org/abs/2504.08802 · HTML: https://mlsanity.com/paper/2504.08802/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 8 Apr 2025.

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

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [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)
- [Spatio-Temporal Graph Scattering Transform](https://mlsanity.com/paper/2012.03363/) (2020)
- [Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks](https://mlsanity.com/paper/2201.08932/) (2022)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (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)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)
- [Towards a General Recipe for Combinatorial Optimization with Multi-Filter GNNs](https://mlsanity.com/paper/2405.20543/) (2024)
- [Molecular Graph Generation via Geometric Scattering](https://mlsanity.com/paper/2110.06241/) (2021)
- [Efficient and Stable Graph Scattering Transforms via Pruning](https://mlsanity.com/paper/2001.09882/) (2020)
- [Underwater object classification using scattering transform of sonar signals](https://mlsanity.com/paper/1707.03133/) (2017)
- [Hyperedge Representations with Hypergraph Wavelets: Applications to Spatial Transcriptomics](https://mlsanity.com/paper/2409.09469/) (2024)
- [Stability of the scattering transform for deformations with minimal regularity](https://mlsanity.com/paper/2205.11142/) (2022)
- [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)
- [Directed Scattering for Knowledge Graph-based Cellular Signaling Analysis](https://mlsanity.com/paper/2309.07813/) (2023)

## Abstract (arXiv)

Diffusion wavelets extract information from graph signals at different scales of resolution by utilizing graph diffusion operators raised to various powers, known as diffusion scales. Traditionally, these scales are chosen to be dyadic integers, 2j. Here, we propose a novel, unsupervised method for selecting the diffusion scales based on ideas from information theory. We then show that our method can be incorporated into wavelet-based GNNs, which are modeled after the geometric scattering transform, via graph classification experiments.