# Are Adversarial Examples Created Equal? A Learnable Weighted Minimax Risk for Robustness under Non-uniform Attacks

arXiv: https://arxiv.org/abs/2010.12989 · HTML: https://mlsanity.com/paper/2010.12989/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2020.

## Built on by (most cited first, 14 of 14)

- [Exploring and Exploiting Decision Boundary Dynamics for Adversarial Robustness](https://mlsanity.com/paper/2302.03015/) (2023)
- [Dynamic Loss-Based Sample Reweighting for Improved Large Language Model Pretraining](https://mlsanity.com/paper/2502.06733/) (2025)
- [Revisiting Contrastive Learning through the Lens of Neighborhood Component Analysis: an Integrated Framework](https://mlsanity.com/paper/2112.04468/) (2021)
- [Defending Substitution-Based Profile Pollution Attacks on Sequential Recommenders](https://mlsanity.com/paper/2207.11237/) (2022)
- [Outlier Robust Adversarial Training](https://mlsanity.com/paper/2309.05145/) (2023)
- [Learning Sample Reweighting for Accuracy and Adversarial Robustness](https://mlsanity.com/paper/2210.11513/) (2022)
- [Identifying Adversarially Attackable and Robust Samples](https://mlsanity.com/paper/2301.12896/) (2023)
- [Unsupervised Domain Adaptation for COVID-19 Information Service with Contrastive Adversarial Domain Mixup](https://mlsanity.com/paper/2210.03250/) (2022)
- [Certified Defense via Latent Space Randomized Smoothing with Orthogonal Encoders](https://mlsanity.com/paper/2108.00491/) (2021)
- [LoReUn: Data Itself Implicitly Provides Cues to Improve Machine Unlearning](https://mlsanity.com/paper/2507.22499/) (2025)
- [Level Up with ML Vulnerability Identification: Leveraging Domain Constraints in Feature Space for Robust Android Malware Detection](https://mlsanity.com/paper/2205.15128/) (2022)
- [Sample Attackability in Natural Language Adversarial Attacks](https://mlsanity.com/paper/2306.12043/) (2023)
- [Doubly Robust Instance-Reweighted Adversarial Training](https://mlsanity.com/paper/2308.00311/) (2023)
- [Improving Adversarial Training using Vulnerability-Aware Perturbation Budget](https://mlsanity.com/paper/2403.04070/) (2024)

## Abstract (arXiv)

Adversarial Training is proved to be an efficient method to defend against adversarial examples, being one of the few defenses that withstand strong attacks. However, traditional defense mechanisms assume a uniform attack over the examples according to the underlying data distribution, which is apparently unrealistic as the attacker could choose to focus on more vulnerable examples. We present a weighted minimax risk optimization that defends against non-uniform attacks, achieving robustness against adversarial examples under perturbed test data distributions. Our modified risk considers importance weights of different adversarial examples and focuses adaptively on harder examples that are wrongly classified or at higher risk of being classified incorrectly. The designed risk allows the training process to learn a strong defense through optimizing the importance weights. The experiments show that our model significantly improves state-of-the-art adversarial accuracy under non-uniform attacks without a significant drop under uniform attacks.