mlsanityData to 7 Oct 2026

On the Minimal Adversarial Perturbation for Deep Neural Networks with Provable Estimation Error

arXiv 2201.01235 ↗First posted 4 Jan 2022cs.LG cs.AI math.DGcited by 6

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Abstract (arXiv)

Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has opened an interesting research line on provable techniques capable of quantifying the robustness of a given input. In this regard, the Euclidean distance of the input from the classification boundary denotes a well-proved robustness assessment as the minimal affordable adversarial perturbation. Unfortunately, computing such a distance is highly complex due the non-convex nature of NNs. Despite several methods have been proposed to address this issue, to the best of our knowledge, no provable results have been presented to estimate and bound the error committed. This paper addresses this issue by proposing two lightweight strategies to find the minimal adversarial perturbation. Differently from the state-of-the-art, the proposed approach allows formulating an error estimation theory of the approximate distance with respect to the theoretical one. Finally, a substantial set of experiments is reported to evaluate the performance of the algorithms and support the theoretical findings. The obtained results show that the proposed strategies approximate the theoretical distance for samples close to the classification boundary, leading to provable robustness guarantees against any adversarial attacks.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 34 of its 57 references that are in the map. First posted on arXiv 4 Jan 2022.

Builds on

34 of 57 references.

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22 more
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Cited by year

Citing papers per year: 2022: 2; 2023: 0; 2024: 1; 2025: 3.

6 papers.

  1. 2022Defending From Physically-Realizable Adversarial Attacks Through Internal Over-Activation Analysiscited by 10
  2. 2022Robust-by-Design Classification via Unitary-Gradient Neural Networkscited by 4
  3. 2024Transcending Adversarial Perturbations: Manifold-Aided Adversarial Examples with Legitimate Semanticscited by 4
  4. 2025Benchmarking the Spatial Robustness of DNNs via Natural and Adversarial Localized Corruptionscited by 3
  5. 2025Leveraging Knowledge Graphs and LLMs for Structured Generation of Misinformationcited by 0
  6. 2025Exploiting Edge Features for Transferable Adversarial Attacks in Distributed Machine Learningcited by 0