mlsanityData to 14 Oct 2026

On Spectral Properties of Gradient-based Explanation Methods

arXiv 2508.10595 ↗First posted 14 Aug 2025cs.LG cs.AI cs.CVcited by 2

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Abstract (arXiv)

Understanding the behavior of deep networks is crucial to increase our confidence in their results. Despite an extensive body of work for explaining their predictions, researchers have faced reliability issues, which can be attributed to insufficient formalism. In our research, we adopt novel probabilistic and spectral perspectives to formally analyze explanation methods. Our study reveals a pervasive spectral bias stemming from the use of gradient, and sheds light on some common design choices that have been discovered experimentally, in particular, the use of squared gradient and input perturbation. We further characterize how the choice of perturbation hyperparameters in explanation methods, such as SmoothGrad, can lead to inconsistent explanations and introduce two remedies based on our proposed formalism: (i) a mechanism to determine a standard perturbation scale, and (ii) an aggregation method which we call SpectralLens. Finally, we substantiate our theoretical results through quantitative evaluations.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 39 of its 62 references that are in the map. First posted on arXiv 14 Aug 2025.

Builds on

39 of 62 references.

References · 39

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
  3. 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,733
  4. 2017A Unified Approach to Interpreting Model Predictionscited by 6,555
  5. 2017Axiomatic Attribution for Deep Networkscited by 3,384
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  7. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
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  10. 2018On the Spectral Bias of Neural Networkscited by 1,341
  11. 2018Sanity Checks for Saliency Mapscited by 1,156
  12. 2017SmoothGrad: removing noise by adding noisecited by 1,109
27 more
  1. 2018RISE: Randomized Input Sampling for Explanation of Black-box Modelscited by 838
  2. 2019Deep Double Descent: Where Bigger Models and More Data Hurtcited by 672
  3. 2017Interpretable Explanations of Black Boxes by Meaningful Perturbationcited by 612
  4. 2017The (Un)reliability of saliency methodscited by 333
  5. 2018On the Robustness of Interpretability Methodscited by 314
  6. 2016Not Just a Black Box: Learning Important Features Through Propagating Activation Differencescited by 297
  7. 2019Understanding Deep Networks via Extremal Perturbations and Smooth Maskscited by 259
  8. 2018Learning to Explain: An Information-Theoretic Perspective on Model Interpretationcited by 248
  9. 2020Explaining by Removing: A Unified Framework for Model Explanationcited by 218
  10. 2019Towards Understanding the Spectral Bias of Deep Learningcited by 174
  11. 2022The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspectivecited by 159
  12. 2017The Shattered Gradients Problem: If resnets are the answer, then what is the question?cited by 157
  13. 2020Frequency Bias in Neural Networks for Input of Non-Uniform Densitycited by 140
  14. 2020True to the Model or True to the Data?cited by 126
  15. 2020Reliable Post hoc Explanations: Modeling Uncertainty in Explainabilitycited by 125
  16. 2022A Consistent and Efficient Evaluation Strategy for Attribution Methodscited by 102
  17. 2022Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post Hoc Explanationscited by 77
  18. 2021Seeing Implicit Neural Representations as Fourier Seriescited by 50
  19. 2018Explanation Methods in Deep Learning: Users, Values, Concerns and Challengescited by 49
  20. 2019Why are Saliency Maps Noisy? Cause of and Solution to Noisy Saliency Mapscited by 34
  21. 2021NoiseGrad: Enhancing Explanations by Introducing Stochasticity to Model Weightscited by 28
  22. 2021Probabilistic Sufficient Explanationscited by 24
  23. 2021Cartoon Explanations of Image Classifierscited by 15
  24. 2023Theoretical Behavior of XAI Methods in the Presence of Suppressor Variablescited by 12
  25. 2023On the Lipschitz Constant of Deep Networks and Double Descentcited by 11
  26. 2022Explaining Image Classifiers with Multiscale Directional Image Representationcited by 7
  27. 2023Disagreement amongst counterfactual explanations: How transparency can be deceptivecited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Explanation of Dynamic Physical Field Predictions using WassersteinGrad: Application to Autoregressive Weather Forecastingcited by 0
  2. 2026Improving Adversarial Robustness of Attribution via Implicit Regularizationcited by 0