[Paper Review] Adversarial Robustness with Non-uniform Perturbations

Ecenaz Erdemir, Jeffrey Bickford+2 more|arXiv (Cornell University)|Feb 24, 2021

Adversarial Robustness in Machine Learning42 references4 citations

TL;DR

This paper proposes adversarial training with non-uniform perturbations that account for feature correlations and importance in real-world applications like malware detection, credit risk, and spam filtering. By using a transformation matrix Ω to define non-uniform ℓp-norm constraints, the method achieves significantly higher robustness against realistic attacks compared to uniform perturbations, with up to 94.5% defense success rate on spam detection under strong attacks.

ABSTRACT

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.

Motivation & Objective

• To address the limitation of uniform norm-bounded perturbations in real-world security applications where feature dependencies and semantic constraints exist.
• To improve adversarial robustness in domains like malware detection, credit risk prediction, and spam detection by modeling realistic perturbation constraints.
• To develop a certification framework for non-uniform perturbations that provides stronger theoretical guarantees than uniform bounds.
• To demonstrate that non-uniform adversarial training generalizes better against standard uniform attacks, enhancing practical robustness.

Proposed method

• Introduces a transformed perturbation constraint ||Ωδ||_p ≤ ε, where Ω encodes feature correlations, importance, and domain knowledge.
• Uses Mahalanobis distance (MD), SHAP values, and Pearson correlation to construct Ω, reflecting data distribution characteristics.
• Applies adversarial training with non-uniform constraints, optimizing the model to be robust under realistic perturbation patterns.
• Proposes a hybrid defense (Combo) that enforces both non-uniform and uniform norm constraints to balance robustness and generalization.
• Employs robustness certification via non-uniform perturbation bounds, enabling theoretical guarantees under structured perturbations.
• Validates the approach on real-world datasets for malware, credit risk, and spam detection using PGD attacks and defense success rates.

Experimental results

Research questions

• RQ1 Can non-uniform perturbations that reflect real-world feature dependencies improve adversarial robustness in security-critical applications?
• RQ2 How does adversarial training with non-uniform constraints compare to standard uniform norm-bounded training under realistic attacks?
• RQ3 Can non-uniform perturbation bounds enable stronger robustness certification than uniform bounds?
• RQ4 Does the proposed method generalize to standard uniform attacks, indicating broader practical utility?
• RQ5 What role do feature importance and correlation play in constructing effective non-uniform perturbation constraints?

Key findings

• On the spam detection dataset, the non-uniform method with Mahalanobis-based Ω (NU-δ-MD) achieved a defense success rate of 94.45% under ε=1.5, outperforming the uniform baseline (93.22%) and the Combo defense (94.27% for ε=1.5).
• For malware classification, the non-uniform approach with MD-based Ω reached 92.6% robust accuracy under ε=0.5, significantly outperforming the uniform baseline (89.6%) and other non-uniform variants.
• In credit risk prediction, the NU-δ-MD variant achieved 89.4% robust accuracy at ε=0.7, surpassing the uniform baseline (87.3%) and other non-uniform configurations.
• The non-uniform defense consistently outperformed the uniform baseline across all attack radii in the spam detection use-case, with the largest gap at ε=0.7 (87.7% vs. 86.5% for NU-δ-MD vs. Uniform-δ).
• The Combo defense, which combines non-uniform and uniform constraints, showed intermediate performance, confirming that the non-uniform component is essential for improved robustness.
• Robustness certification using non-uniform bounds was shown to be tighter and more effective than uniform bounds, demonstrating theoretical advantages.