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Neural Collapse refers to the curious phenomenon in the end of training of a neural network, where feature vectors and classification weights converge to a very simple geometrical arrangement (a simplex).
Support-vector networks
Corinna Cortes and Vladimir Vapnik · 1995
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Boosting the margin: A new explanation for the effectiveness of voting methods
Robert E. Schapire, Yoav Freund, Peter Barlett, and Wee Sun Lee · 1997
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Robustness and regularization of support vector machines
Huan Xu, Constantine Caramanis, and Shie Mannor · 2009
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Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2014
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Explaining and harnessing adversarial examples
Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy · 2015
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Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro · 2015
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Nicholas Carlini and David A. Wagner · 2017
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Adversarial examples in the physical world
Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio · 2017
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Universal adversarial perturbations
Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, Omar Fawzi, and Pascal Frossard · 2017
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Practical black-box attacks against machine learning
Nicolas Papernot, Patrick D. McDaniel, Ian J. Goodfellow, Somesh Jha, Z. Berkay Celik, and Ananthram Swami · 2017
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The implicit bias of gradient descent on separable data
Daniel Soudry, Elad Hoffer, Mor Shpigel Nacson, Suriya Gunasekar, and Nathan Srebro · 2018
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Ali Shafahi, Mahyar Najibi, Amin Ghiasi, Zheng Xu, John P. Dickerson, Christoph Studer, Larry S. Davis, Gavin Taylor, and Tom Goldstein · 2019
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Theoretically principled trade-off between robustness and accuracy
Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P. Xing, Laurent El Ghaoui, and Michael I. Jordan · 2019
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Implicit bias of gradient descent based adversarial training on separable data
Yan Li, Ethan X. Fang, Huan Xu, and Tuo Zhao · 2020
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Gradient descent maximizes the margin of homogeneous neural networks
Kaifeng Lyu and Jian Li · 2020
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Prevalence of neural collapse during the terminal phase of deep learning training
Vardan Papyan, XY Han, and David L Donoho · 2020
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Overfitting in adversarially robust deep learning
Leslie Rice, Eric Wong, and J. Zico Kolter · 2020
On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
Weinan E and Stephan Wojtowytsch · 2022
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Neural collapse under MSE loss: Proximity to and dynamics on the central path
X.Y. Han, Vardan Papyan, and David L. Donoho · 2022
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A law of data separation in deep learning
Hangfeng He and Weijie J. Su · 2022
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Limitations of neural collapse for understanding generalization in deep learning
Like Hui, Mikhail Belkin, and Preetum Nakkiran · 2022
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An unconstrained layer-peeled perspective on neural collapse
Wenlong Ji, Yiping Lu, Yiliang Zhang, Zhun Deng, and Weijie J Su · 2022
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Fast is better than free: Revisiting adversarial training
Eric Wong, Leslie Rice, and J. Zico Kolter · 2020
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Robustbench: a standardized adversarial robustness benchmark
Francesco Croce, Maksym Andriushchenko, Vikash Sehwag, Edoardo Debenedetti, Nicolas Flammarion, Mung Chiang, Prateek Mittal, and Matthias Hein · 2021
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Exploring deep neural networks via layer-peeled model: Minority collapse in imbalanced training
Cong Fang, Hangfeng He, Qi Long, and Weijie J. Su · 2021
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On the role of neural collapse in transfer learning
Tomer Galanti, András György, and Marcus Hutter · 2021
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A geometric analysis of neural collapse with unconstrained features
Zhihui Zhu, Tianyu Ding, Jinxin Zhou, Xiao Li, Chong You, Jeremias Sulam, and Qing Qu · 2021
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Nearest class-center simplification through intermediate layers
Ido Ben-Shaul and Shai Dekel · 2022
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Xiao Li, Sheng Liu, Jinxin Zhou, Xinyu Lu, Carlos Fernandez-Granda, Zhihui Zhu, and Qing Qu · 2022
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Implicit bias of adversarial training for deep neural networks
Bochen Lv and Zhanxing Zhu · 2022
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Neural collapse with unconstrained features
Dustin G. Mixon, Hans Parshall, and Jianzong Pi · 2022
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Extended unconstrained features model for exploring deep neural collapse
Tom Tirer and Joan Bruna · 2022
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Perturbation analysis of neural collapse
Tom Tirer, Haoxiang Huang, and Jonathan Niles-Weed · 2022
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On the optimization landscape of neural collapse under MSE loss: Global optimality with unconstrained features
Jinxin Zhou, Xiao Li, Tianyu Ding, Chong You, Qing Qu, and Zhihui Zhu · 2022
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Feature learning in deep classifiers through intermediate neural collapse
Akshay Rangamani, Marius Lindegaard, Tomer Galanti, and Tomaso Poggio · 2023
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