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Data-Driven Lipschitz Continuity: A Cost-Effective Approach to Improve Adversarial Robustness

Erh-Chung Chen, Pin-Yu Chen, I-Hsin Chung, Che-Rung Lee

TL;DR

This paper tackles the high computational cost of achieving adversarial robustness by introducing a data-driven remapping strategy grounded in Lipschitz continuity. By inserting a forged function that shrinks input domains and binding the Lipschitz constant $k_F$ with a per-layer design, the method provides robustness comparable to data-intensive adversarial training but with a single dataset pass and no gradient estimation. The approach is compatible with existing training pipelines, substantially reducing training time and enabling scalability, while empirical results on CIFAR-10/100 and ImageNet show improved robustness across architectures and attacks. Practically, this work offers a cost-effective defense that can be integrated into current frameworks to achieve strong protection against adversarial perturbations without requiring extensive extra data. $

Abstract

As deep neural networks (DNNs) are increasingly deployed in sensitive applications, ensuring their security and robustness has become critical. A major threat to DNNs arises from adversarial attacks, where small input perturbations can lead to incorrect predictions. Recent advances in adversarial training improve robustness by incorporating additional examples from external datasets or generative models. However, these methods often incur high computational costs, limiting their practicality and hindering real-world deployment. In this paper, we propose a cost-efficient alternative based on Lipschitz continuity that achieves robustness comparable to models trained with extensive supplementary data. Unlike conventional adversarial training, our method requires only a single pass over the dataset without gradient estimation, making it highly efficient. Furthermore, our method can integrate seamlessly with existing adversarial training frameworks and enhances the robustness of models without requiring extra generative data. Experimental results show that our approach not only reduces computational overhead but also maintains or improves the defensive capabilities of robust neural networks. This work opens a promising direction for developing practical, scalable defenses against adversarial attacks.

Data-Driven Lipschitz Continuity: A Cost-Effective Approach to Improve Adversarial Robustness

TL;DR

This paper tackles the high computational cost of achieving adversarial robustness by introducing a data-driven remapping strategy grounded in Lipschitz continuity. By inserting a forged function that shrinks input domains and binding the Lipschitz constant with a per-layer design, the method provides robustness comparable to data-intensive adversarial training but with a single dataset pass and no gradient estimation. The approach is compatible with existing training pipelines, substantially reducing training time and enabling scalability, while empirical results on CIFAR-10/100 and ImageNet show improved robustness across architectures and attacks. Practically, this work offers a cost-effective defense that can be integrated into current frameworks to achieve strong protection against adversarial perturbations without requiring extensive extra data. $

Abstract

As deep neural networks (DNNs) are increasingly deployed in sensitive applications, ensuring their security and robustness has become critical. A major threat to DNNs arises from adversarial attacks, where small input perturbations can lead to incorrect predictions. Recent advances in adversarial training improve robustness by incorporating additional examples from external datasets or generative models. However, these methods often incur high computational costs, limiting their practicality and hindering real-world deployment. In this paper, we propose a cost-efficient alternative based on Lipschitz continuity that achieves robustness comparable to models trained with extensive supplementary data. Unlike conventional adversarial training, our method requires only a single pass over the dataset without gradient estimation, making it highly efficient. Furthermore, our method can integrate seamlessly with existing adversarial training frameworks and enhances the robustness of models without requiring extra generative data. Experimental results show that our approach not only reduces computational overhead but also maintains or improves the defensive capabilities of robust neural networks. This work opens a promising direction for developing practical, scalable defenses against adversarial attacks.
Paper Structure (20 sections, 2 theorems, 15 equations, 3 figures, 11 tables, 1 algorithm)

This paper contains 20 sections, 2 theorems, 15 equations, 3 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Adversarial Attacks
  4. Defensive Strategies
  5. Methodology
  6. Lipschitz Continuity
  7. Forged Function
  8. Data-driven Algorithm
  9. Experiments
  10. Setup
  11. White-box Evaluation
  12. Cost Analysis
  13. Gradient Masking Verification
  14. Discussion
  15. Conclusion
  16. ...and 5 more sections

Key Result

Theorem 1

(Gershgorin Circle Theorem) For an $m \times m$ matrix $A$ with entries $a_{ij}$, each eigenvalue of $A$ is in at least one of the disk:

Figures (3)

  • Figure 1: Insertion points of the forged function. In ConvNets, it is inserted into the residual blocks, while in Transformers, it is inserted into the MLP layers.
  • Figure 2: Certified robustness that conducted by random smoothing.
  • Figure 3: The average proportion of pruned activations depends on the location of each linear layer. FC1 and FC2 refer to the first and second fully connected layers in MLP blocks, respectively.

Theorems & Definitions (3)

  • Theorem 1
  • Lemma 2
  • proof