mlsanityData to 7 Oct 2026

SPADE: A Spectral Method for Black-Box Adversarial Robustness Evaluation

arXiv 2102.03716 ↗First posted 7 Feb 2021cs.LG cs.AI cs.CVcited by 16

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Abstract (arXiv)

A black-box spectral method is introduced for evaluating the adversarial robustness of a given machine learning (ML) model. Our approach, named SPADE, exploits bijective distance mapping between the input/output graphs constructed for approximating the manifolds corresponding to the input/output data. By leveraging the generalized Courant-Fischer theorem, we propose a SPADE score for evaluating the adversarial robustness of a given model, which is proved to be an upper bound of the best Lipschitz constant under the manifold setting. To reveal the most non-robust data samples highly vulnerable to adversarial attacks, we develop a spectral graph embedding procedure leveraging dominant generalized eigenvectors. This embedding step allows assigning each data sample a robustness score that can be further harnessed for more effective adversarial training. Our experiments show the proposed SPADE method leads to promising empirical results for neural network models that are adversarially trained with the MNIST and CIFAR-10 data sets.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 34 of its 55 references that are in the map. First posted on arXiv 7 Feb 2021.

Builds on

34 of 55 references.

References · 34

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22 more
  1. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 368
  2. 2017Parseval Networks: Improving Robustness to Adversarial Examplescited by 288
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 8; 2025: 2; 2026: 2.

16 papers.

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  1. 2022GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networkscited by 14
  2. 2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
  3. 2024Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attackscited by 9
  4. 2024SAGMAN: Stability Analysis of Graph Neural Networks on the Manifoldscited by 4
  5. 2024RobustBlack: Challenging Black-Box Adversarial Attacks on State-of-the-Art Defensescited by 2
  6. 2025SALMAN: Stability Analysis of Language Models Through the Maps Between Graph-based Manifoldscited by 1
  7. 2026Which Graph Shift Operator? A Spectral Answer to an Empirical Questioncited by 1
  8. 2023Graph-based methods coupled with specific distributional distances for adversarial attack detectioncited by 0
  9. 2023Evaluating Adversarial Robustness with Expected Viable Performancecited by 0
  10. 2024Mitigating the Impact of Noisy Edges on Graph-Based Algorithms via Adversarial Robustness Evaluationcited by 0
  11. 2024SGM-PINN: Sampling Graphical Models for Faster Training of Physics-Informed Neural Networkscited by 0
  12. 2024Adversarial-Robustness-Guided Graph Pruningcited by 0
4 more
  1. 2024Defending Collaborative Filtering Recommenders via Adversarial Robustness Based Edge Reweightingcited by 0
  2. 2024Spectrally unstable nodes drive reliability failures in graph learningcited by 0
  3. 2025Pruning Graphs by Adversarial Robustness Evaluation to Strengthen GNN Defensescited by 0
  4. 2026Spectral structural distortion reveals redundant neurons in neural networkscited by 0