mlsanityData to 14 Oct 2026

Simplicity Bias of Two-Layer Networks beyond Linearly Separable Data

arXiv 2405.17299 ↗First posted 27 May 2024stat.ML cs.LG math.OCcited by 11

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Abstract (arXiv)

Simplicity bias, the propensity of deep models to over-rely on simple features, has been identified as a potential reason for limited out-of-distribution generalization of neural networks (Shah et al., 2020). Despite the important implications, this phenomenon has been theoretically confirmed and characterized only under strong dataset assumptions, such as linear separability (Lyu et al., 2021). In this work, we characterize simplicity bias for general datasets in the context of two-layer neural networks initialized with small weights and trained with gradient flow. Specifically, we prove that in the early training phases, network features cluster around a few directions that do not depend on the size of the hidden layer. Furthermore, for datasets with an XOR-like pattern, we precisely identify the learned features and demonstrate that simplicity bias intensifies during later training stages. These results indicate that features learned in the middle stages of training may be more useful for OOD transfer. We support this hypothesis with experiments on image data.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 47 of its 57 references that are in the map. First posted on arXiv 27 May 2024.

Builds on

47 of 57 references.

References · 47

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,333
  3. 2020Shortcut Learning in Deep Neural Networkscited by 1,969
  4. 2018ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustnesscited by 1,432
  5. 2018On the Spectral Bias of Neural Networkscited by 1,341
  6. 2017A Closer Look at Memorization in Deep Networkscited by 942
  7. 2019Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inferencecited by 876
  8. 2018On Lazy Training in Differentiable Programmingcited by 675
  9. 2019Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networkscited by 566
  10. 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 466
  11. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 426
  12. 2020The Pitfalls of Simplicity Bias in Neural Networkscited by 351
35 more
  1. 2019Gradient Descent Maximizes the Margin of Homogeneous Neural Networkscited by 320
  2. 2019SGD on Neural Networks Learns Functions of Increasing Complexitycited by 204
  3. 2018Deep learning generalizes because the parameter-function map is biased towards simple functionscited by 183
  4. 2020Directional convergence and alignment in deep learningcited by 178
  5. 2018Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balancedcited by 177
  6. 2018Training behavior of deep neural network in frequency domaincited by 174
  7. 2022High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representationcited by 150
  8. 2020Frequency Bias in Neural Networks for Input of Non-Uniform Densitycited by 140
  9. 2018Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernelcited by 131
  10. 2020What shapes feature representations? Exploring datasets, architectures, and trainingcited by 126
  11. 2021Gradient Descent on Two-layer Nets: Margin Maximization and Simplicity Biascited by 83
  12. 2022Distilling Model Failures as Directions in Latent Spacecited by 82
  13. 2023Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokkingcited by 80
  14. 2017SGD Learns Over-parameterized Networks that Provably Generalize on Linearly Separable Datacited by 79
  15. 2022Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputscited by 76
  16. 2020Phase diagram for two-layer ReLU neural networks at infinite-width limitcited by 67
  17. 2022Neural networks trained with SGD learn distributions of increasing complexitycited by 50
  18. 2019Theory of the Frequency Principle for General Deep Neural Networkscited by 46
  19. 2022Implicit Bias in Leaky ReLU Networks Trained on High-Dimensional Datacited by 46
  20. 2022Random Feature Amplification: Feature Learning and Generalization in Neural Networkscited by 35
  21. 2021On Margin Maximization in Linear and ReLU Networkscited by 34
  22. 2021Towards Understanding the Condensation of Neural Networks at Initial Trainingcited by 32
  23. 2023Early Neuron Alignment in Two-layer ReLU Networks with Small Initializationcited by 28
  24. 2023Over-Parameterization Exponentially Slows Down Gradient Descent for Learning a Single Neuroncited by 25
  25. 2022On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Biascited by 21
  26. 2021Understanding Deflation Process in Over-parametrized Tensor Decompositioncited by 20
  27. 2021Towards Understanding Learning in Neural Networks with Linear Teacherscited by 19
  28. 2023Implicit Bias of Gradient Descent for Two-layer ReLU and Leaky ReLU Networks on Nearly-orthogonal Datacited by 18
  29. 2024Early alignment in two-layer networks training is a two-edged swordcited by 18
  30. 2023Learning a Neuron by a Shallow ReLU Network: Dynamics and Implicit Bias for Correlated Inputscited by 16
  31. 2023Understanding Multi-phase Optimization Dynamics and Rich Nonlinear Behaviors of ReLU Networkscited by 15
  32. 2020An analytic theory of shallow networks dynamics for hinge loss classificationcited by 14
  33. 2022Agnostic Learning of General ReLU Activation Using Gradient Descentcited by 12
  34. 2022Adversarial Reprogramming Revisitedcited by 10
  35. 2022Implicit Bias of MSE Gradient Optimization in Underparameterized Neural Networkscited by 9

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 7; 2026: 2.

11 papers.

  1. 2025Saddle-to-Saddle Dynamics Explains A Simplicity Bias Across Neural Network Architecturescited by 15
  2. 2025Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wildcited by 13
  3. 2024Simplicity bias and optimization threshold in two-layer ReLU networkscited by 11
  4. 2024ALTA: Compiler-Based Analysis of Transformerscited by 7
  5. 2025Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformerscited by 6
  6. 2026Implicit Bias of Mirror Flow in Homogeneous Neural Networks: Sparse and Dense Feature Learningcited by 3
  7. 2025Review of Hallucination Understanding in Large Language and Vision Modelscited by 2
  8. 2025Neural Collapse under Gradient Flow on Shallow ReLU Networks for Orthogonally Separable Datacited by 2
  9. 2025On Measuring Localization of Shortcuts in Deep Networkscited by 1
  10. 2025A Critical Review of Predominant Bias in Neural Networkscited by 0
  11. 2026Noise Stability of Transformer Modelscited by 0