mlsanityData to 14 Oct 2026

A law of adversarial risk, interpolation, and label noise

arXiv 2207.03933 ↗First posted 8 Jul 2022stat.ML cs.CR cs.LGcited by 8

Not on the map. Why?

Abstract (arXiv)

In supervised learning, it has been shown that label noise in the data can be interpolated without penalties on test accuracy. We show that interpolating label noise induces adversarial vulnerability, and prove the first theorem showing the relationship between label noise and adversarial risk for any data distribution. Our results are almost tight if we do not make any assumptions on the inductive bias of the learning algorithm. We then investigate how different components of this problem affect this result, including properties of the distribution. We also discuss non-uniform label noise distributions; and prove a new theorem showing uniform label noise induces nearly as large an adversarial risk as the worst poisoning with the same noise rate. Then, we provide theoretical and empirical evidence that uniform label noise is more harmful than typical real-world label noise. Finally, we show how inductive biases amplify the effect of label noise and argue the need for future work in this direction.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 37 of its 48 references that are in the map. First posted on arXiv 8 Jul 2022.

Builds on

37 of 48 references.

References · 37

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  4. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,385
  5. 2016Adversarial examples in the physical worldcited by 1,769
  6. 2016Understanding deep learning requires rethinking generalizationcited by 1,674
  7. 2017Ensemble Adversarial Training: Attacks and Defensescited by 840
  8. 2015Distillation as a Defense to Adversarial Perturbations against Deep Neural Networkscited by 678
  9. 2019Benign Overfitting in Linear Regressioncited by 549
  10. 2019Surprises in High-Dimensional Ridgeless Least Squares Interpolationcited by 513
  11. 2020What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimationcited by 497
  12. 2019Does Learning Require Memorization? A Short Tale about a Long Tailcited by 460
25 more
  1. 2017Wild Patterns: Ten Years After the Rise of Adversarial Machine Learningcited by 414
  2. 2020The Pitfalls of Simplicity Bias in Neural Networkscited by 351
  3. 2018Stronger generalization bounds for deep nets via a compression approachcited by 307
  4. 2017Parseval Networks: Improving Robustness to Adversarial Examplescited by 293
  5. 2021Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotationscited by 256
  6. 2018Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learningcited by 225
  7. 2019SGD on Neural Networks Learns Functions of Increasing Complexitycited by 204
  8. 2021A Universal Law of Robustness via Isoperimetrycited by 151
  9. 2020Classification vs regression in overparameterized regimes: Does the loss function matter?cited by 97
  10. 2022Can Neural Nets Learn the Same Model Twice? Investigating Reproducibility and Double Descent from the Decision Boundary Perspectivecited by 57
  11. 2020A law of robustness for two-layers neural networkscited by 55
  12. 2018On the Geometry of Adversarial Examplescited by 43
  13. 2021The Dimpled Manifold Model of Adversarial Examples in Machine Learningcited by 41
  14. 2020How benign is benign overfitting?cited by 40
  15. 2016A General Characterization of the Statistical Query Complexitycited by 27
  16. 2022Indiscriminate Data Poisoning Attacks on Neural Networkscited by 25
  17. 2019Neural networks are a priori biased towards Boolean functions with low entropycited by 24
  18. 2022Fast Rates for Noisy Interpolation Require Rethinking the Effects of Inductive Biascited by 22
  19. 2021Understanding the Interaction of Adversarial Training with Noisy Labelscited by 19
  20. 2022How unfair is private learning ?cited by 18
  21. 2020Neural Anisotropy Directionscited by 17
  22. 2021Analysing the Noise Model Error for Realistic Noisy Label Datacited by 14
  23. 2018Robustness via Deep Low-Rank Representationscited by 11
  24. 2021Fundamental tradeoffs between memorization and robustness in random features and neural tangent regimescited by 9
  25. 2017Multiscale sequence modeling with a learned dictionarycited by 6

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 5.

8 papers.

  1. 2024Corrective Machine Unlearningcited by 29
  2. 2022Unsupervised Learning under Latent Label Shiftcited by 9
  3. 2024Reliable Model Watermarking: Defending Against Theft without Compromising on Evasioncited by 9
  4. 2024Accuracy on the wrong line: On the pitfalls of noisy data for out-of-distribution generalisationcited by 9
  5. 2023Regularly Truncated M-estimators for Learning with Noisy Labelscited by 8
  6. 2024The Role of Learning Algorithms in Collective Actioncited by 8
  7. 2023Annealing Self-Distillation Rectification Improves Adversarial Trainingcited by 7
  8. 2024A Cognac Shot To Forget Bad Memories: Corrective Unlearning for Graph Neural Networkscited by 2