mlsanityData to 14 Oct 2026

How Spurious Features Are Memorized: Precise Analysis for Random and NTK Features

arXiv 2305.12100 ↗First posted 20 May 2023stat.ML cs.LGcited by 11

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Abstract (arXiv)

Deep learning models are known to overfit and memorize spurious features in the training dataset. While numerous empirical studies have aimed at understanding this phenomenon, a rigorous theoretical framework to quantify it is still missing. In this paper, we consider spurious features that are uncorrelated with the learning task, and we provide a precise characterization of how they are memorized via two separate terms: (i) the stability of the model with respect to individual training samples, and (ii) the feature alignment between the spurious feature and the full sample. While the first term is well established in learning theory and it is connected to the generalization error in classical work, the second one is, to the best of our knowledge, novel. Our key technical result gives a precise characterization of the feature alignment for the two prototypical settings of random features (RF) and neural tangent kernel (NTK) regression. We prove that the memorization of spurious features weakens as the generalization capability increases and, through the analysis of the feature alignment, we unveil the role of the model and of its activation function. Numerical experiments show the predictive power of our theory on standard datasets (MNIST, CIFAR-10).

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 50 of its 64 references that are in the map. First posted on arXiv 20 May 2023.

Builds on

50 of 64 references.

References · 50

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  2. 2020Shortcut Learning in Deep Neural Networkscited by 1,969
  3. 2018ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustnesscited by 1,432
  4. 2017A Closer Look at Memorization in Deep Networkscited by 942
  5. 2018On Lazy Training in Differentiable Programmingcited by 675
  6. 2019Deep Double Descent: Where Bigger Models and More Data Hurtcited by 672
  7. 2019Benign Overfitting in Linear Regressioncited by 549
  8. 2020What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimationcited by 497
  9. 2019Does Learning Require Memorization? A Short Tale about a Long Tailcited by 460
  10. 2019The generalization error of random features regression: Precise asymptotics and double descent curvecited by 413
  11. 2020The Pitfalls of Simplicity Bias in Neural Networkscited by 351
  12. 2020Noise or Signal: The Role of Image Backgrounds in Object Recognitioncited by 343
38 more
  1. 2020An Investigation of Why Overparameterization Exacerbates Spurious Correlationscited by 310
  2. 2021Deep learning: a statistical viewpointcited by 240
  3. 2019SGD on Neural Networks Learns Functions of Increasing Complexitycited by 204
  4. 2019Stolen Memories: Leveraging Model Memorization for Calibrated White-Box Membership Inferencecited by 175
  5. 2019Linearized two-layers neural networks in high dimensioncited by 155
  6. 2021A Universal Law of Robustness via Isoperimetrycited by 151
  7. 2021Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolationcited by 132
  8. 2017Theoretical insights into the optimization landscape of over-parameterized shallow neural networkscited by 128
  9. 2020What shapes feature representations? Exploring datasets, architectures, and trainingcited by 126
  10. 2021Learning curves of generic features maps for realistic datasets with a teacher-student modelcited by 126
  11. 2021Salient ImageNet: How to discover spurious features in Deep Learning?cited by 114
  12. 2020The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalizationcited by 101
  13. 2015Algorithmic Stability for Adaptive Data Analysiscited by 88
  14. 2018Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path?cited by 88
  15. 2020Tight Bounds on the Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networkscited by 87
  16. 2020The Interpolation Phase Transition in Neural Networks: Memorization and Generalization under Lazy Trainingcited by 84
  17. 2017A Random Matrix Approach to Neural Networkscited by 80
  18. 2020Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networkscited by 77
  19. 2017The loss surface of deep and wide neural networkscited by 74
  20. 2021On the geometry of generalization and memorization in deep neural networkscited by 73
  21. 2020Global Convergence of Deep Networks with One Wide Layer Followed by Pyramidal Topologycited by 66
  22. 2021Examining and Combating Spurious Features under Distribution Shiftcited by 65
  23. 2015On the relation between accuracy and fairness in binary classificationcited by 48
  24. 2020Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixturescited by 47
  25. 2021Finding and Fixing Spurious Patterns with Explanationscited by 38
  26. 2022Memorization and Optimization in Deep Neural Networks with Minimum Over-parameterizationcited by 36
  27. 2021Towards Robust Classification Model by Counterfactual and Invariant Data Generationcited by 30
  28. 2022Understanding Rare Spurious Correlations in Neural Networkscited by 27
  29. 2021Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networkscited by 21
  30. 2022What Can the Neural Tangent Kernel Tell Us About Adversarial Robustness?cited by 21
  31. 2022Information-Theoretic Bias Reduction via Causal View of Spurious Correlationcited by 15
  32. 2022Evolution of Neural Tangent Kernels under Benign and Adversarial Trainingcited by 14
  33. 2023Understanding Reconstruction Attacks with the Neural Tangent Kernel and Dataset Distillationcited by 14
  34. 2023Beyond the Universal Law of Robustness: Sharper Laws for Random Features and Neural Tangent Kernelscited by 13
  35. 2022Measures of Information Reflect Memorization Patternscited by 12
  36. 2022On the (Non-)Robustness of Two-Layer Neural Networks in Different Learning Regimescited by 11
  37. 2022How Biased are Your Features?: Computing Fairness Influence Functions with Global Sensitivity Analysiscited by 7
  38. 2022Towards Differential Relational Privacy and its use in Question Answeringcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 3; 2026: 2.

11 papers.

  1. 2023A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networkscited by 49
  2. 2024The Clever Hans Mirage: A Comprehensive Survey on Spurious Correlations in Machine Learningcited by 41
  3. 2024The Pitfalls of Memorization: When Memorization Hurts Generalizationcited by 19
  4. 2023Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approachcited by 9
  5. 2024NTK-Guided Few-Shot Class Incremental Learningcited by 7
  6. 2024Towards Understanding the Word Sensitivity of Attention Layers: A Study via Random Featurescited by 5
  7. 2025ShortcutProbe: Probing Prediction Shortcuts for Learning Robust Modelscited by 5
  8. 2025A Law of Data Reconstruction for Random Features (and Beyond)cited by 3
  9. 2025Review of Hallucination Understanding in Large Language and Vision Modelscited by 2
  10. 2026Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descentcited by 0
  11. 2026Mitigating Spurious Correlations with Memorization-Guided Dataset De-Biasingcited by 0