# Adversarial Robustness of Supervised Sparse Coding

arXiv: https://arxiv.org/abs/2010.12088 · HTML: https://mlsanity.com/paper/2010.12088/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 22 of 22)

- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Learning sparse features can lead to overfitting in neural networks](https://mlsanity.com/paper/2206.12314/) (2022)
- [Predify: Augmenting deep neural networks with brain-inspired predictive coding dynamics](https://mlsanity.com/paper/2106.02749/) (2021)
- [Revisiting Sparse Convolutional Model for Visual Recognition](https://mlsanity.com/paper/2210.12945/) (2022)
- [Adversarial robustness of sparse local Lipschitz predictors](https://mlsanity.com/paper/2202.13216/) (2022)
- [Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustness](https://mlsanity.com/paper/2309.16096/) (2023)
- [Sparsity-aware generalization theory for deep neural networks](https://mlsanity.com/paper/2307.00426/) (2023)
- [Understanding Noise-Augmented Training for Randomized Smoothing](https://mlsanity.com/paper/2305.04746/) (2023)
- [Adversarial for Good? How the Adversarial ML Community's Values Impede Socially Beneficial Uses of Attacks](https://mlsanity.com/paper/2107.10302/) (2021)
- [Can Implicit Bias Imply Adversarial Robustness?](https://mlsanity.com/paper/2405.15942/) (2024)
- [A Non-negative VAE:the Generalized Gamma Belief Network](https://mlsanity.com/paper/2408.03388/) (2024)
- [Improved Training of Sparse Coding Variational Autoencoder via Weight Normalization](https://mlsanity.com/paper/2101.09453/) (2021)
- [Robust width: A lightweight and certifiable adversarial defense](https://mlsanity.com/paper/2405.15971/) (2024)
- [Sensitivity of sparse codes to image distortions](https://mlsanity.com/paper/2204.07466/) (2022)
- [Structural Extensions of Basis Pursuit: Guarantees on Adversarial Robustness](https://mlsanity.com/paper/2205.08955/) (2022)
- [On The Relationship Between Universal Adversarial Attacks And Sparse Representations](https://mlsanity.com/paper/2311.08265/) (2023)
- [An NMF-Based Building Block for Interpretable Neural Networks With Continual Learning](https://mlsanity.com/paper/2311.11485/) (2023)
- [Golyadkin's Torment: Doppelg"angers and Adversarial Vulnerability](https://mlsanity.com/paper/2410.13193/) (2024)
- [Multi-Dictionary Learning for Low Rank Sparse Coding](https://mlsanity.com/paper/2509.10033/) (2025)
- [Triggering hallucinations in model-based MRI reconstruction via adversarial perturbations](https://mlsanity.com/paper/2602.18536/) (2026)

## Abstract (arXiv)

Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in practice. In this work, we strike a better balance by considering a model that involves learning a representation while at the same time giving a precise generalization bound and a robustness certificate. We focus on the hypothesis class obtained by combining a sparsity-promoting encoder coupled with a linear classifier, and show an interesting interplay between the expressivity and stability of the (supervised) representation map and a notion of margin in the feature space. We bound the robust risk (to ℓ2-bounded perturbations) of hypotheses parameterized by dictionaries that achieve a mild encoder gap on training data. Furthermore, we provide a robustness certificate for end-to-end classification. We demonstrate the applicability of our analysis by computing certified accuracy on real data, and compare with other alternatives for certified robustness.