mlsanityData to 14 Oct 2026

Adaptive Smoothness-weighted Adversarial Training for Multiple Perturbations with Its Stability Analysis

arXiv 2210.00557 ↗First posted 2 Oct 2022cs.LGcited by 9

Not on the map. Why?

Abstract (arXiv)

Adversarial Training (AT) has been demonstrated as one of the most effective methods against adversarial examples. While most existing works focus on AT with a single type of perturbation e.g., the ℓ_∞ attacks), DNNs are facing threats from different types of adversarial examples. Therefore, adversarial training for multiple perturbations (ATMP) is proposed to generalize the adversarial robustness over different perturbation types (in ℓ1, ℓ2, and ℓ_∞ norm-bounded perturbations). However, the resulting model exhibits trade-off between different attacks. Meanwhile, there is no theoretical analysis of ATMP, limiting its further development. In this paper, we first provide the smoothness analysis of ATMP and show that ℓ1, ℓ2, and ℓ_∞ adversaries give different contributions to the smoothness of the loss function of ATMP. Based on this, we develop the stability-based excess risk bounds and propose adaptive smoothness-weighted adversarial training for multiple perturbations. Theoretically, our algorithm yields better bounds. Empirically, our experiments on CIFAR10 and CIFAR100 achieve the state-of-the-art performance against the mixture of multiple perturbations attacks.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 23 of its 31 references that are in the map. First posted on arXiv 2 Oct 2022.

Builds on

23 of 31 references.

References · 23

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  3. 2013Intriguing properties of neural networkscited by 5,155
  4. 2016Identity Mappings in Deep Residual Networkscited by 1,965
  5. 2018Averaging Weights Leads to Wider Optima and Better Generalizationcited by 1,209
  6. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
  7. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 574
  8. 2020On Adaptive Attacks to Adversarial Example Defensescited by 555
  9. 2015Train faster, generalize better: Stability of stochastic gradient descentcited by 552
  10. 2018Adversarially Robust Generalization Requires More Datacited by 318
  11. 2020Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examplescited by 278
  12. 2018A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decaycited by 226
11 more
  1. 2019Adversarial Training and Robustness for Multiple Perturbationscited by 183
  2. 2018Rademacher Complexity for Adversarially Robust Generalizationcited by 132
  3. 2019Adversarial Training Can Hurt Generalizationcited by 132
  4. 2021On the Convergence and Robustness of Adversarial Trainingcited by 130
  5. 2019Adversarial Robustness Against the Union of Multiple Perturbation Modelscited by 88
  6. 2020On the Loss Landscape of Adversarial Training: Identifying Challenges and How to Overcome Themcited by 59
  7. 2019Convergence of Adversarial Training in Overparametrized Neural Networkscited by 58
  8. 2021Relating Adversarially Robust Generalization to Flat Minimacited by 57
  9. 2020Adversarial Learning Guarantees for Linear Hypotheses and Neural Networkscited by 47
  10. 2020On the Generalization Properties of Adversarial Trainingcited by 23
  11. 2020Approximate Manifold Defense Against Multiple Adversarial Perturbationscited by 7

Built on by

Cited by year

Citing papers per year: 2022: 2; 2023: 0; 2024: 5; 2025: 2.

9 papers.

  1. 2022Stability Analysis and Generalization Bounds of Adversarial Trainingcited by 30
  2. 2022Adversarial Rademacher Complexity of Deep Neural Networkscited by 18
  3. 2024Uniformly Stable Algorithms for Adversarial Training and Beyondcited by 2
  4. 2024RAMP: Boosting Adversarial Robustness Against Multiple lp Perturbations for Universal Robustnesscited by 1
  5. 2024Towards Generalized Certified Robustness with Multi-Norm Trainingcited by 1
  6. 2025PRBench: A Standardized Probabilistic Robustness Benchmarkcited by 1
  7. 2024Better Representations via Adversarial Training in Pre-Training: A Theoretical Perspectivecited by 0
  8. 2024Bridging the Gap: Rademacher Complexity in Robust and Standard Generalizationcited by 0
  9. 2025How to Enhance Downstream Adversarial Robustness (almost) without Touching the Pre-Trained Foundation Model?cited by 0