# Scattering Networks for Hybrid Representation Learning

arXiv: https://arxiv.org/abs/1809.06367 · HTML: https://mlsanity.com/paper/1809.06367/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2018.

## Built on by (most cited first, 30 of 33)

- [Parametric Scattering Networks](https://mlsanity.com/paper/2107.09539/) (2021)
- [Tune It or Don't Use It: Benchmarking Data-Efficient Image Classification](https://mlsanity.com/paper/2108.13122/) (2021)
- [Spectral Leakage and Rethinking the Kernel Size in CNNs](https://mlsanity.com/paper/2101.10143/) (2021)
- [ScatSimCLR: self-supervised contrastive learning with pretext task regularization for small-scale datasets](https://mlsanity.com/paper/2108.13939/) (2021)
- [The Unreasonable Effectiveness of Patches in Deep Convolutional Kernels Methods](https://mlsanity.com/paper/2101.07528/) (2021)
- [Improving Differentially Private SGD via Randomly Sparsified Gradients](https://mlsanity.com/paper/2112.00845/) (2021)
- [Occam's Razor for Self Supervised Learning: What is Sufficient to Learn Good Representations?](https://mlsanity.com/paper/2406.10743/) (2024)
- [Self-Supervised Pretraining for Differentially Private Learning](https://mlsanity.com/paper/2206.07125/) (2022)
- [Genetic Programming-Based Evolutionary Deep Learning for Data-Efficient Image Classification](https://mlsanity.com/paper/2209.13233/) (2022)
- [Differentially Private Deep Learning with ModelMix](https://mlsanity.com/paper/2210.03843/) (2022)
- [Image Classification with Small Datasets: Overview and Benchmark](https://mlsanity.com/paper/2212.12478/) (2022)
- [Riesz feature representation: scale equivariant scattering network for classification tasks](https://mlsanity.com/paper/2307.08467/) (2023)
- [Tackling the Accuracy-Interpretability Trade-off in a Hierarchy of Machine Learning Models for the Prediction of Extreme Heatwaves](https://mlsanity.com/paper/2410.00984/) (2024)
- [Random Feature Representation Boosting](https://mlsanity.com/paper/2501.18283/) (2025)
- [Deep Neural Networks with Efficient Guaranteed Invariances](https://mlsanity.com/paper/2303.01567/) (2023)
- [Efficient Hybrid Network: Inducting Scattering Features](https://mlsanity.com/paper/2203.15392/) (2022)
- [Differentiable Time-Frequency Scattering on GPU](https://mlsanity.com/paper/2204.08269/) (2022)
- [Predict better with less training data using a QNN](https://mlsanity.com/paper/2206.03960/) (2022)
- [MV-MR: multi-views and multi-representations for self-supervised learning and knowledge distillation](https://mlsanity.com/paper/2303.12130/) (2023)
- [No Data Augmentation? Alternative Regularizations for Effective Training on Small Datasets](https://mlsanity.com/paper/2309.01694/) (2023)
- [Hierarchical Invariance for Robust and Interpretable Vision Tasks at Larger Scales](https://mlsanity.com/paper/2402.15430/) (2024)
- [Bottom-Up Scattering Information Perception Network for SAR target recognition](https://mlsanity.com/paper/2504.04780/) (2025)
- [The Maximal Overlap Discrete Wavelet Scattering Transform and Its Application in Classification Tasks](https://mlsanity.com/paper/2506.12039/) (2025)
- [AdaDPIGU: Differentially Private SGD with Adaptive Clipping and Importance-Based Gradient Updates for Deep Neural Networks](https://mlsanity.com/paper/2507.06525/) (2025)
- [CXR-Net: An Artificial Intelligence Pipeline for Quick Covid-19 Screening of Chest X-Rays](https://mlsanity.com/paper/2103.00087/) (2021)
- [Wavelet Design in a Learning Framework](https://mlsanity.com/paper/2107.11225/) (2021)
- [Modelling nonlinear dependencies in the latent space of inverse scattering](https://mlsanity.com/paper/2203.10307/) (2022)
- [Attention-Based Scattering Network for Satellite Imagery](https://mlsanity.com/paper/2210.12185/) (2022)
- [ExplainFix: Explainable Spatially Fixed Deep Networks](https://mlsanity.com/paper/2303.10408/) (2023)
- [Mean-Field Microcanonical Gradient Descent](https://mlsanity.com/paper/2403.08362/) (2024)

## Abstract (arXiv)

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve competitive results both for supervised and unsupervised learning tasks, while making progress towards constructing more interpretable CNNs. For supervised learning, we demonstrate that the early layers of CNNs do not necessarily need to be learned, and can be replaced with a scattering network instead. Indeed, using hybrid architectures, we achieve the best results with predefined representations to-date, while being competitive with end-to-end learned CNNs. Specifically, even applying a shallow cascade of small-windowed scattering coefficients followed by 1×1-convolutions results in AlexNet accuracy on the ILSVRC2012 classification task. Moreover, by combining scattering networks with deep residual networks, we achieve a single-crop top-5 error of 11.4% on ILSVRC2012. Also, we show they can yield excellent performance in the small sample regime on CIFAR-10 and STL-10 datasets, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. For unsupervised learning, scattering coefficients can be a competitive representation that permits image recovery. We use this fact to train hybrid GANs to generate images. Finally, we empirically analyze several properties related to stability and reconstruction of images from scattering coefficients.