# Parametric Scattering Networks

arXiv: https://arxiv.org/abs/2107.09539 · HTML: https://mlsanity.com/paper/2107.09539/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 131 references that are in the map.
- First posted on arXiv 20 Jul 2021.

## Builds on (most cited first, 30 of 59)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [COVID-Net: A Tailored Deep Convolutional Neural Network Design for Detection of COVID-19 Cases from Chest X-Ray Images](https://mlsanity.com/paper/2003.09871/) (2020)
- [Super-Convergence: Very Fast Training of Neural Networks Using Large Learning Rates](https://mlsanity.com/paper/1708.07120/) (2017)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [An Empirical Survey of Data Augmentation for Limited Data Learning in NLP](https://mlsanity.com/paper/2106.07499/) (2021)
- [Data Augmentation by Pairing Samples for Images Classification](https://mlsanity.com/paper/1801.02929/) (2018)
- [Understanding Deep Convolutional Networks](https://mlsanity.com/paper/1601.04920/) (2016)
- [Deep-COVID: Predicting COVID-19 From Chest X-Ray Images Using Deep Transfer Learning](https://mlsanity.com/paper/2004.09363/) (2020)
- [Sliced Wasserstein Kernels for Probability Distributions](https://mlsanity.com/paper/1511.03198/) (2015)
- [Kymatio: Scattering Transforms in Python](https://mlsanity.com/paper/1812.11214/) (2018)
- [Deep Scattering Spectrum](https://mlsanity.com/paper/1304.6763/) (2013)
- [Rigid-Motion Scattering for Texture Classification](https://mlsanity.com/paper/1403.1687/) (2014)
- [Deep Roto-Translation Scattering for Object Classification](https://mlsanity.com/paper/1412.8659/) (2014)

## Built on by (most cited first, 16 of 16)

- [Neural Fourier Filter Bank](https://mlsanity.com/paper/2212.01735/) (2022)
- [Occam's Razor for Self Supervised Learning: What is Sufficient to Learn Good Representations?](https://mlsanity.com/paper/2406.10743/) (2024)
- [ChimeraMix: Image Classification on Small Datasets via Masked Feature Mixing](https://mlsanity.com/paper/2202.11616/) (2022)
- [Riesz feature representation: scale equivariant scattering network for classification tasks](https://mlsanity.com/paper/2307.08467/) (2023)
- [On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networks](https://mlsanity.com/paper/2209.11740/) (2022)
- [Differentiable Time-Frequency Scattering on GPU](https://mlsanity.com/paper/2204.08269/) (2022)
- [No Data Augmentation? Alternative Regularizations for Effective Training on Small Datasets](https://mlsanity.com/paper/2309.01694/) (2023)
- [From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets](https://mlsanity.com/paper/2212.00394/) (2022)
- [Invariant Scattering Transform for Medical Imaging](https://mlsanity.com/paper/2307.04771/) (2023)
- [Learnable wavelet neural networks for cosmological inference](https://mlsanity.com/paper/2307.14362/) (2023)
- [Scattering Networks on Noncommutative Finite Groups](https://mlsanity.com/paper/2505.20950/) (2025)
- [Learning Object-Centric Representations in SAR Images with Multi-Level Feature Fusion](https://mlsanity.com/paper/2509.09298/) (2025)
- [SCRAPL: Scattering Transform with Random Paths for Machine Learning](https://mlsanity.com/paper/2602.11145/) (2026)
- [Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data](https://mlsanity.com/paper/2603.20908/) (2026)
- [Transversal Pooling Neural Networks](https://mlsanity.com/paper/2609.36237/) (2026)
- [Specific Algorithmic Interpretability of Neural Networks: A Case Study on Textures](https://mlsanity.com/paper/2610.04413/) (2026)

## Abstract (arXiv)

The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to outperform learned representations in certain tasks, particularly on limited labeled data and highly structured signals. The wavelet filters used in the scattering transform are typically selected to create a tight frame via a parameterized mother wavelet. In this work, we investigate whether this standard wavelet filterbank construction is optimal. Focusing on Morlet wavelets, we propose to learn the scales, orientations, and aspect ratios of the filters to produce problem-specific parameterizations of the scattering transform. We show that our learned versions of the scattering transform yield significant performance gains in small-sample classification settings over the standard scattering transform. Moreover, our empirical results suggest that traditional filterbank constructions may not always be necessary for scattering transforms to extract effective representations.