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Neural collapse with unconstrained features

arXiv 2011.11619 ↗First posted 23 Nov 2020cs.LGcited by 140

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Abstract (arXiv)

Neural collapse is an emergent phenomenon in deep learning that was recently discovered by Papyan, Han and Donoho. We propose a simple "unconstrained features model" in which neural collapse also emerges empirically. By studying this model, we provide some explanation for the emergence of neural collapse in terms of the landscape of empirical risk.

Key facts. Cited by 140 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Nov 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 22; 2023: 32; 2024: 31; 2025: 22; 2026: 24.

140 papers.

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  1. 2021A Geometric Analysis of Neural Collapse with Unconstrained Featurescited by 226
  2. 2021Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Trainingcited by 166
  3. 2021Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Pathcited by 156
  4. 2023Investigating the Catastrophic Forgetting in Multimodal Large Language Modelscited by 119
  5. 2023Neural Collapse Inspired Feature-Classifier Alignment for Few-Shot Class Incremental Learningcited by 112
  6. 2022Extended Unconstrained Features Model for Exploring Deep Neural Collapsecited by 101
  7. 2021On the Role of Neural Collapse in Transfer Learningcited by 100
  8. 2022Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?cited by 100
  9. 2022On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Featurescited by 97
  10. 2022Neural Collapse: A Review on Modelling Principles and Generalizationcited by 95
  11. 2021An Unconstrained Layer-Peeled Perspective on Neural Collapsecited by 87
  12. 2022Imbalance Trouble: Revisiting Neural-Collapse Geometrycited by 80
38 more
  1. 2022Are All Losses Created Equal: A Neural Collapse Perspectivecited by 78
  2. 2021Label-Imbalanced and Group-Sensitive Classification under Overparameterizationcited by 74
  3. 2024Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimizationcited by 66
  4. 2022Limitations of Neural Collapse for Understanding Generalization in Deep Learningcited by 63
  5. 2022Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifoldcited by 50
  6. 2023Understanding Imbalanced Semantic Segmentation Through Neural Collapsecited by 46
  7. 2022Neural Collapse Inspired Attraction-Repulsion-Balanced Loss for Imbalanced Learningcited by 43
  8. 2023Deep Neural Collapse Is Provably Optimal for the Deep Unconstrained Features Modelcited by 43
  9. 2021Benign Overfitting in Multiclass Classification: All Roads Lead to Interpolationcited by 41
  10. 2023NECO: NEural Collapse Based Out-of-distribution detectioncited by 41
  11. 2023Generalized Neural Collapse for a Large Number of Classescited by 39
  12. 2023Neural Collapse for Unconstrained Feature Model under Cross-entropy Loss with Imbalanced Datacited by 38
  13. 2024Linguistic Collapse: Neural Collapse in (Large) Language Modelscited by 36
  14. 2022Perturbation Analysis of Neural Collapsecited by 34
  15. 2022Improving Self-Supervised Learning by Characterizing Idealized Representationscited by 33
  16. 2023Detecting Out-of-Distribution Through the Lens of Neural Collapsecited by 33
  17. 2023Towards a Unified Theoretical Understanding of Non-contrastive Learning via Rank Differential Mechanismcited by 32
  18. 2025On the Effect of Negative Gradient in Group Relative Deep Reinforcement Optimizationcited by 31
  19. 2022Grokking phase transitions in learning local rules with gradient descentcited by 28
  20. 2022The Asymmetric Maximum Margin Bias of Quasi-Homogeneous Neural Networkscited by 25
  21. 2022Understanding and Improving Transfer Learning of Deep Models via Neural Collapsecited by 24
  22. 2024Implicit Geometry of Next-token Prediction: From Language Sparsity Patterns to Model Representationscited by 24
  23. 2022Linking Neural Collapse and L2 Normalization with Improved Out-of-Distribution Detection in Deep Neural Networkscited by 23
  24. 2023On the Implicit Geometry of Cross-Entropy Parameterizations for Label-Imbalanced Datacited by 23
  25. 2023A Message Passing Perspective on Learning Dynamics of Contrastive Learningcited by 22
  26. 2024Average gradient outer product as a mechanism for deep neural collapsecited by 21
  27. 2024The Prevalence of Neural Collapse in Neural Multivariate Regressioncited by 21
  28. 2022Nearest Class-Center Simplification through Intermediate Layerscited by 20
  29. 2023Neural Collapse in the Intermediate Hidden Layers of Classification Neural Networkscited by 20
  30. 2023A Neural Collapse Perspective on Feature Evolution in Graph Neural Networkscited by 19
  31. 2023Neural (Tangent Kernel) Collapsecited by 18
  32. 2024Neural Collapse versus Low-rank Bias: Is Deep Neural Collapse Really Optimal?cited by 16
  33. 2025How Muon's Spectral Design Benefits Generalization: A Study on Imbalanced Datacited by 16
  34. 2024Learning Equi-angular Representations for Online Continual Learningcited by 15
  35. 2023Generalizing and Decoupling Neural Collapse via Hyperspherical Uniformity Gapcited by 14
  36. 2023Neural Collapse Terminus: A Unified Solution for Class Incremental Learning and Its Variantscited by 14
  37. 2023Neural Collapse in Multi-label Learning with Pick-all-label Losscited by 14
  38. 2024Implicit Optimization Bias of Next-Token Prediction in Linear Modelscited by 14

50 most cited of 140 All 140 (JSON)