mlsanityData to 7 Oct 2026

ε-weakened Robustness of Deep Neural Networks

arXiv 2110.15764 ↗First posted 29 Oct 2021cs.LG cs.AIcited by 8

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Abstract (arXiv)

This paper introduces a notation of varepsilon-weakened robustness for analyzing the reliability and stability of deep neural networks (DNNs). Unlike the conventional robustness, which focuses on the "perfect" safe region in the absence of adversarial examples, varepsilon-weakened robustness focuses on the region where the proportion of adversarial examples is bounded by user-specified varepsilon. Smaller varepsilon means a smaller chance of failure. Under such robustness definition, we can give conclusive results for the regions where conventional robustness ignores. We prove that the varepsilon-weakened robustness decision problem is PP-complete and give a statistical decision algorithm with user-controllable error bound. Furthermore, we derive an algorithm to find the maximum varepsilon-weakened robustness radius. The time complexity of our algorithms is polynomial in the dimension and size of the network. So, they are scalable to large real-world networks. Besides, We also show its potential application in analyzing quality issues.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 33 of its 58 references that are in the map. First posted on arXiv 29 Oct 2021.

Builds on

33 of 58 references.

References · 33

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21 more
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Built on by

Cited by year

Citing papers per year: 2022: 3; 2023: 3; 2024: 2.

8 papers.

  1. 2022Accurate Fairness: Improving Individual Fairness without Trading Accuracycited by 16
  2. 2023How adversarial attacks can disrupt seemingly stable accurate classifierscited by 4
  3. 2023A Tale of Two Approximations: Tightening Over-Approximation for DNN Robustness Verification via Under-Approximationcited by 2
  4. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 2
  5. 2022Tightening Robustness Verification of MaxPool-based Neural Networks via Minimizing the Over-Approximation Zonecited by 1
  6. 2023Topology-preserving Adversarial Training for Alleviating Natural Accuracy Degradationcited by 1
  7. 2022DualApp: Tight Over-Approximation for Neural Network Robustness Verification via Under-Approximationcited by 0
  8. 2024Patch Synthesis for Property Repair of Deep Neural Networkscited by 0