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Neural collapse (NC) is a phenomenon that emerges at the terminal phase of the training (TPT) of deep neural networks (DNNs).
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
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Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
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Deep residual learning for image recognition
K. He, X. Zhang, S. Ren, and J. Sun · 2016
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Convergence analysis of two-layer neural networks with ReLU activation
Y. Li and Y. Yuan · 2017
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Gradient descent provably optimizes over-parameterized neural networks
S. S. Du, X. Zhai, B. Poczos, and A. Singh · 2018
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A mean field view of the landscape of two-layer neural networks
S. Mei, A. Montanari, and P.-M. Nguyen · 2018
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The implicit bias of gradient descent on separable data
D. Soudry, E. Hoffer, M. S. Nacson, S. Gunasekar, and N. Srebro · 2018
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High-dimensional Probability: An Introduction with Applications in Data Science
R. Vershynin · 2018
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High-dimensional Statistics: A Non-asymptotic Viewpoint
M. J. Wainwright · 2019
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Prevalence of neural collapse during the terminal phase of deep learning training
V. Papyan, X. Han, and D. L. Donoho · 2020
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Exploring deep neural networks via layer-peeled model: Minority collapse in imbalanced training
C. Fang, H. He, Q. Long, and W. J. Su · 2021
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On the role of neural collapse in transfer learning
T. Galanti, A. György, and M. Hutter · 2021
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Neural collapse under MSE loss: Proximity to and dynamics on the central path
X. Han, V. Papyan, and D. L. Donoho · 2021
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Explicit regularization and implicit bias in deep network classifiers trained with the square loss
T. Poggio and Q. Liao · 2021
Cited alongside, same era.
A geometric analysis of neural collapse with unconstrained features
Z. Zhu, T. Ding, J. Zhou, X. Li, C. You, J. Sulam, and Q. Qu · 2021
Cited alongside, same era.
On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
W. E and S. Wojtowytsch · 2022
Cited alongside, same era.
Limitations of neural collapse for understanding generalization in deep learning
L. Hui, M. Belkin, and P. Nakkiran · 2022
Cited alongside, same era.
An unconstrained layer-peeled perspective on neural collapse
W. Ji, Y. Lu, Y. Zhang, Z. Deng, and W. J. Su · 2022
Cited alongside, same era.
Neural collapse with normalized features: A geometric analysis over the riemannian manifold
C. Yaras, P. Wang, Z. Zhu, L. Balzano, and Q. Qu · 2022
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On the optimization landscape of neural collapse under mse loss: Global optimality with unconstrained features
J. Zhou, X. Li, T. Ding, C. You, Q. Qu, and Z. Zhu · 2022
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On the implicit geometry of cross-entropy parameterizations for label-imbalanced data
T. Behnia, G. R. Kini, V. Vakilian, and C. Thrampoulidis · 2023
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Neural collapse in deep linear network: From balanced to imbalanced data
H. Dang, T. Nguyen, T. Tran, H. Tran, and N. Ho · 2023
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Neural collapse in deep linear networks: from balanced to imbalanced data
H. Dang, T. Tran, S. Osher, H. Tran-The, N. Ho, and T. Nguyen · 2023
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V. Kothapalli, E. Rasromani, and V. Awatramani · 2022
Cited alongside, same era.
Principled and efficient transfer learning of deep models via neural collapse
X. Li, S. Liu, J. Zhou, X. Lu, C. Fernandez-Granda, Z. Zhu, and Q. Qu · 2022
Cited alongside, same era.
Neural collapse under cross-entropy loss
J. Lu and S. Steinerberger · 2022
Cited alongside, same era.
Neural collapse with unconstrained features
D. G. Mixon, H. Parshall, and J. Pi · 2022
Cited alongside, same era.
Neural collapse in deep homogeneous classifiers and the role of weight decay
A. Rangamani and A. Banburski-Fahey · 2022
Cited alongside, same era.
Trainability and accuracy of artificial neural networks: An interacting particle system approach
G. Rotskoff and E. Vanden-Eijnden · 2022
Cited alongside, same era.
Imbalance trouble: Revisiting neural-collapse geometry
C. Thrampoulidis, G. R. Kini, V. Vakilian, and T. Behnia · 2022
Cited alongside, same era.
Memorization-dilation: Modeling neural collapse under noise
D. A. Nguyen, R. Levie, J. Lienen, E. Hüllermeier, and G. Kutyniok · 2023
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Perturbation analysis of neural collapse
T. Tirer, H. Huang, and J. Niles-Weed · 2023
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Are neurons actually collapsed? on the fine-grained structure in neural representations
Y. Yang, J. Steinhardt, and W. Hu · 2023
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Neural collapse for cross-entropy class-imbalanced learning with unconstrained ReLU feature model
H. Dang, T. Tran, T. Nguyen, and N. Ho · 2024
Closest in time.
C. Garrod and J. P. Keating · 2024
Closest in time.
Neural collapse for unconstrained feature model under cross-entropy loss with imbalanced data
W. Hong and S. Ling · 2024
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Neural (tangent kernel) collapse
M. Seleznova, D. Weitzner, R. Giryes, G. Kutyniok, and H.-H. Chou · 2024
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Deep neural collapse is provably optimal for the deep unconstrained features model
P. Súkeník, M. Mondelli, and C. H. Lampert · 2024
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