mlsanityData to 7 Oct 2026

Generalization Properties of Adversarial Training for ℓ0-Bounded Adversarial Attacks

arXiv 2402.03576 ↗First posted 5 Feb 2024cs.LG cs.CRcited by 0

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Abstract (arXiv)

We have widely observed that neural networks are vulnerable to small additive perturbations to the input causing misclassification. In this paper, we focus on the ℓ0-bounded adversarial attacks, and aim to theoretically characterize the performance of adversarial training for an important class of truncated classifiers. Such classifiers are shown to have strong performance empirically, as well as theoretically in the Gaussian mixture model, in the ℓ0-adversarial setting. The main contribution of this paper is to prove a novel generalization bound for the binary classification setting with ℓ0-bounded adversarial perturbation that is distribution-independent. Deriving a generalization bound in this setting has two main challenges: (i) the truncated inner product which is highly non-linear; and (ii) maximization over the ℓ0 ball due to adversarial training is non-convex and highly non-smooth. To tackle these challenges, we develop new coding techniques for bounding the combinatorial dimension of the truncated hypothesis class.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 21 of its 34 references that are in the map. First posted on arXiv 5 Feb 2024.

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21 of 34 references.

References · 21

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  4. 2019Is BERT Really Robust? A Strong Baseline for Natural Language Attack on Text Classification and Entailmentcited by 663
  5. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  6. 2018Adversarially Robust Generalization Requires More Datacited by 318
  7. 2018Certified Defenses against Adversarial Examplescited by 305
  8. 2019Adversarial Training Can Hurt Generalizationcited by 131
  9. 2018Towards the first adversarially robust neural network model on MNISTcited by 104
  10. 2019VC Classes are Adversarially Robustly Learnable, but Only Improperlycited by 83
  11. 2019Adversarial camera stickers: A physical camera-based attack on deep learning systemscited by 69
  12. 2020Sparse-RS: a versatile framework for query-efficient sparse black-box adversarial attackscited by 65
9 more
  1. 2016Adversarial Perturbations Against Deep Neural Networks for Malware Classificationcited by 42
  2. 2019A Simple Explanation for the Existence of Adversarial Examples with Small Hamming Distancecited by 32
  3. 2020On the Generalization Properties of Adversarial Trainingcited by 23
  4. 2020On the Rademacher Complexity of Linear Hypothesis Setscited by 17
  5. 2018Adversarial Risk Bounds via Function Transformationcited by 12
  6. 2021Consistent Non-Parametric Methods for Maximizing Robustnesscited by 7
  7. 2021Robust Classification Under ℓ0 Attack for the Gaussian Mixture Modelcited by 5
  8. 2020Sample Complexity of Adversarially Robust Linear Classification on Separated Datacited by 3
  9. 2022Efficient and Robust Classification for Sparse Attackscited by 1

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