mlsanityData to 7 Oct 2026

On the Structural Sensitivity of Deep Convolutional Networks to the Directions of Fourier Basis Functions

arXiv 1809.04098 ↗First posted 11 Sep 2018cs.CVcited by 31

Not on the map. Why?

Abstract (arXiv)

Data-agnostic quasi-imperceptible perturbations on inputs are known to degrade recognition accuracy of deep convolutional networks severely. This phenomenon is considered to be a potential security issue. Moreover, some results on statistical generalization guarantees indicate that the phenomenon can be a key to improve the networks' generalization. However, the characteristics of the shared directions of such harmful perturbations remain unknown. Our primal finding is that convolutional networks are sensitive to the directions of Fourier basis functions. We derived the property by specializing a hypothesis of the cause of the sensitivity, known as the linearity of neural networks, to convolutional networks and empirically validated it. As a by-product of the analysis, we propose an algorithm to create shift-invariant universal adversarial perturbations available in black-box settings.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Sep 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 8; 2023: 5; 2024: 4; 2025: 3; 2026: 2.

31 papers.

Sort:

By area:

  1. 2023On the Foundations of Shortcut Learningcited by 64
  2. 2021SpectralDefense: Detecting Adversarial Attacks on CNNs in the Fourier Domaincited by 30
  3. 2021A Frequency Perspective of Adversarial Robustnesscited by 28
  4. 2021Relative stability toward diffeomorphisms indicates performance in deep netscited by 12
  5. 2022How Does Frequency Bias Affect the Robustness of Neural Image Classifiers against Common Corruption and Adversarial Perturbations?cited by 11
  6. 2021Detecting AutoAttack Perturbations in the Frequency Domaincited by 10
  7. 2024FACL-Attack: Frequency-Aware Contrastive Learning for Transferable Adversarial Attackscited by 8
  8. 2022Fourier-Based Augmentations for Improved Robustness and Uncertainty Calibrationcited by 7
  9. 2023Linear CNNs Discover the Statistical Structure of the Dataset Using Only the Most Dominant Frequenciescited by 7
  10. 2021Real-time Detection of Practical Universal Adversarial Perturbationscited by 6
  11. 2021Bridging the Gap Between Adversarial Robustness and Optimization Biascited by 5
  12. 2021Frequency Centric Defense Mechanisms against Adversarial Examplescited by 3
19 more
  1. 2022Understanding robustness and generalization of artificial neural networks through Fourier maskscited by 3
  2. 2021F-Drop&Match: GANs with a Dead Zone in the High-Frequency Domaincited by 2
  3. 2022FourierNet: Shape-Preserving Network for Henle's Fiber Layer Segmentation in Optical Coherence Tomography Imagescited by 2
  4. 2024Towards a Novel Perspective on Adversarial Examples Driven by Frequencycited by 2
  5. 2025On the Complexity-Faithfulness Trade-off of Gradient-Based Explanationscited by 2
  6. 2021Simple black-box universal adversarial attacks on medical image classification based on deep neural networkscited by 1
  7. 2022Adversarial amplitude swap towards robust image classifierscited by 1
  8. 2022Robustness and invariance properties of image classifierscited by 1
  9. 2022Universal Adversarial Directionscited by 1
  10. 2022Aliasing is a Driver of Adversarial Attackscited by 1
  11. 2023Fourier Sensitivity and Regularization of Computer Vision Modelscited by 1
  12. 2024Interpreting Global Perturbation Robustness of Image Models using Axiomatic Spectral Importance Decompositioncited by 1
  13. 2024DFT-Based Adversarial Attack Detection in MRI Brain Imaging: Enhancing Diagnostic Accuracy in Alzheimer's Case Studiescited by 1
  14. 2023Exploiting Frequency Spectrum of Adversarial Images for General Robustnesscited by 0
  15. 2023Frequency maps reveal the correlation between Adversarial Attacks and Implicit Biascited by 0
  16. 2025FREQuency ATTribution: benchmarking frequency-based occlusion for time series datacited by 0
  17. 2025Understanding Sensitivity of Differential Attention through the Lens of Adversarial Robustnesscited by 0
  18. 2026How Do Document Parsers Break? Auditing Structural Vulnerability in Document Intelligencecited by 0
  19. 2026Cross-Modal Attention Acts as a Frequency Filter: Why Verbose Prompts Improve Robustness in Vision-Language Modelscited by 0