# The Robust Manifold Defense: Adversarial Training using Generative Models

arXiv: https://arxiv.org/abs/1712.09196 · HTML: https://mlsanity.com/paper/1712.09196/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2017.

## Built on by (most cited first, 30 of 35)

- [Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?](https://mlsanity.com/paper/2104.09425/) (2021)
- [Relating Adversarially Robust Generalization to Flat Minima](https://mlsanity.com/paper/2104.04448/) (2021)
- [Ensembling with Deep Generative Views](https://mlsanity.com/paper/2104.14551/) (2021)
- [The Dimpled Manifold Model of Adversarial Examples in Machine Learning](https://mlsanity.com/paper/2106.10151/) (2021)
- [Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning](https://mlsanity.com/paper/2106.09004/) (2021)
- [Adversarial Robustness with Semi-Infinite Constrained Learning](https://mlsanity.com/paper/2110.15767/) (2021)
- [Probabilistically Robust Learning: Balancing Average- and Worst-case Performance](https://mlsanity.com/paper/2202.01136/) (2022)
- [DiffProtect: Generate Adversarial Examples with Diffusion Models for Facial Privacy Protection](https://mlsanity.com/paper/2305.13625/) (2023)
- [A Review of Adversarial Attack and Defense for Classification Methods](https://mlsanity.com/paper/2111.09961/) (2021)
- [The Many Faces of Adversarial Risk](https://mlsanity.com/paper/2201.08956/) (2022)
- [Towards Robust Neural Networks via Close-loop Control](https://mlsanity.com/paper/2102.01862/) (2021)
- [Predify: Augmenting deep neural networks with brain-inspired predictive coding dynamics](https://mlsanity.com/paper/2106.02749/) (2021)
- [Distributionally Robust Policy Learning via Adversarial Environment Generation](https://mlsanity.com/paper/2107.06353/) (2021)
- [Instruct2Attack: Language-Guided Semantic Adversarial Attacks](https://mlsanity.com/paper/2311.15551/) (2023)
- [Local Competition and Stochasticity for Adversarial Robustness in Deep Learning](https://mlsanity.com/paper/2101.01121/) (2021)
- [Out-of-Distribution Detection with Reconstruction Error and Typicality-based Penalty](https://mlsanity.com/paper/2212.12641/) (2022)
- [Interpolated Joint Space Adversarial Training for Robust and Generalizable Defenses](https://mlsanity.com/paper/2112.06323/) (2021)
- [GenLabel: Mixup Relabeling using Generative Models](https://mlsanity.com/paper/2201.02354/) (2022)
- [Adversarial robustness for latent models: Revisiting the robust-standard accuracies tradeoff](https://mlsanity.com/paper/2110.11950/) (2021)
- [Adversarial Examples Exist in Two-Layer ReLU Networks for Low Dimensional Linear Subspaces](https://mlsanity.com/paper/2303.00783/) (2023)
- [Semantic Perturbations with Normalizing Flows for Improved Generalization](https://mlsanity.com/paper/2108.07958/) (2021)
- [Transcending Adversarial Perturbations: Manifold-Aided Adversarial Examples with Legitimate Semantics](https://mlsanity.com/paper/2402.03095/) (2024)
- [Attribute-Guided Encryption with Facial Texture Masking](https://mlsanity.com/paper/2305.13548/) (2023)
- [Adversarial Machine Learning in Text Analysis and Generation](https://mlsanity.com/paper/2101.08675/) (2021)
- [Robust Training Using Natural Transformation](https://mlsanity.com/paper/2105.04070/) (2021)
- [Adversarial Examples Detection with Bayesian Neural Network](https://mlsanity.com/paper/2105.08620/) (2021)
- [On the role of feedback in visual processing: a predictive coding perspective](https://mlsanity.com/paper/2106.04225/) (2021)
- [FROB: Few-shot ROBust Model for Classification and Out-of-Distribution Detection](https://mlsanity.com/paper/2111.15487/) (2021)
- [Towards Bridging the gap between Empirical and Certified Robustness against Adversarial Examples](https://mlsanity.com/paper/2102.05096/) (2021)
- [Robust Upper Bounds for Adversarial Training](https://mlsanity.com/paper/2112.09279/) (2021)

## Abstract (arXiv)

We propose a new type of attack for finding adversarial examples for image classifiers. Our method exploits spanners, i.e. deep neural networks whose input space is low-dimensional and whose output range approximates the set of images of interest. Spanners may be generators of GANs or decoders of VAEs. The key idea in our attack is to search over latent code pairs to find ones that generate nearby images with different classifier outputs. We argue that our attack is stronger than searching over perturbations of real images. Moreover, we show that our stronger attack can be used to reduce the accuracy of Defense-GAN to 3%, resolving an open problem from the well-known paper by Athalye et al. We combine our attack with normal adversarial training to obtain the most robust known MNIST classifier, significantly improving the state of the art against PGD attacks. Our formulation involves solving a min-max problem, where the min player sets the parameters of the classifier and the max player is running our attack, and is thus searching for adversarial examples in the em low-dimensional input space of the spanner. All code and models are available at urlhttps://github.com/ajiljalal/manifold-defense.git