# Adversarial Robustness with Non-uniform Perturbations

arXiv: https://arxiv.org/abs/2102.12002 · HTML: https://mlsanity.com/paper/2102.12002/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 23 of 23)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [EMBER: An Open Dataset for Training Static PE Malware Machine Learning Models](https://mlsanity.com/paper/1804.04637/) (2018)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [TESSERACT: Eliminating Experimental Bias in Malware Classification across Space and Time](https://mlsanity.com/paper/1807.07838/) (2018)
- [Learning perturbation sets for robust machine learning](https://mlsanity.com/paper/2007.08450/) (2020)
- [Once-for-All Adversarial Training: In-Situ Tradeoff between Robustness and Accuracy for Free](https://mlsanity.com/paper/2010.11828/) (2020)
- [Imperceptible Adversarial Attacks on Tabular Data](https://mlsanity.com/paper/1911.03274/) (2019)
- [Adversarial Deep Ensemble: Evasion Attacks and Defenses for Malware Detection](https://mlsanity.com/paper/2006.16545/) (2020)
- [Improving Robustness of ML Classifiers against Realizable Evasion Attacks Using Conserved Features](https://mlsanity.com/paper/1708.08327/) (2017)
- [Generating End-to-End Adversarial Examples for Malware Classifiers Using Explainability](https://mlsanity.com/paper/2009.13243/) (2020)
- [Not All Datasets Are Born Equal: On Heterogeneous Data and Adversarial Examples](https://mlsanity.com/paper/2010.03180/) (2020)
- [On Certifying Non-uniform Bound against Adversarial Attacks](https://mlsanity.com/paper/1903.06603/) (2019)

## Built on by (most cited first, 17 of 17)

- [A Unified Framework for Adversarial Attack and Defense in Constrained Feature Space](https://mlsanity.com/paper/2112.01156/) (2021)
- [Projected Randomized Smoothing for Certified Adversarial Robustness](https://mlsanity.com/paper/2309.13794/) (2023)
- [Feature Importance Guided Attack: A Model Agnostic Adversarial Attack](https://mlsanity.com/paper/2106.14815/) (2021)
- [Verification of Neural Networks' Global Robustness](https://mlsanity.com/paper/2402.19322/) (2024)
- [Investigating Imperceptibility of Adversarial Attacks on Tabular Data: An Empirical Analysis](https://mlsanity.com/paper/2407.11463/) (2024)
- [TabAttackBench: A Benchmark for Adversarial Attacks on Tabular Data](https://mlsanity.com/paper/2505.21027/) (2025)
- [Living off the Analyst: Harvesting Features from Yara Rules for Malware Detection](https://mlsanity.com/paper/2411.18516/) (2024)
- [Adversarial Attack and Defense for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2202.03077/) (2022)
- [Level Up with ML Vulnerability Identification: Leveraging Domain Constraints in Feature Space for Robust Android Malware Detection](https://mlsanity.com/paper/2205.15128/) (2022)
- [An Overview and Prospective Outlook on Robust Training and Certification of Machine Learning Models](https://mlsanity.com/paper/2208.07464/) (2022)
- [Towards Generating Adversarial Examples on Mixed-type Data](https://mlsanity.com/paper/2210.09405/) (2022)
- [Towards Independence Criterion in Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2403.08124/) (2024)
- [Firenze: Model Evaluation Using Weak Signals](https://mlsanity.com/paper/2207.00827/) (2022)
- [Certified Adversarial Robustness of Machine Learning-based Malware Detectors via (De)Randomized Smoothing](https://mlsanity.com/paper/2405.00392/) (2024)
- [Bypassing DARCY Defense: Indistinguishable Universal Adversarial Triggers](https://mlsanity.com/paper/2409.03183/) (2024)
- [Disentangling Safe and Unsafe Corruptions via Anisotropy and Locality](https://mlsanity.com/paper/2501.18098/) (2025)
- [Insights on Adversarial Attacks for Tabular Machine Learning via a Systematic Literature Review](https://mlsanity.com/paper/2506.15506/) (2025)

## Abstract (arXiv)

Robustness of machine learning models is critical for security related applications, where real-world adversaries are uniquely focused on evading neural network based detectors. Prior work mainly focus on crafting adversarial examples (AEs) with small uniform norm-bounded perturbations across features to maintain the requirement of imperceptibility. However, uniform perturbations do not result in realistic AEs in domains such as malware, finance, and social networks. For these types of applications, features typically have some semantically meaningful dependencies. The key idea of our proposed approach is to enable non-uniform perturbations that can adequately represent these feature dependencies during adversarial training. We propose using characteristics of the empirical data distribution, both on correlations between the features and the importance of the features themselves. Using experimental datasets for malware classification, credit risk prediction, and spam detection, we show that our approach is more robust to real-world attacks. Finally, we present robustness certification utilizing non-uniform perturbation bounds, and show that non-uniform bounds achieve better certification.