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We discuss methods for visualizing neural network decision boundaries and decision regions.
Neural networks and the bias/variance dilemma
Stuart Geman, Elie Bienenstock, and René Doursat · 1992
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Statistical mechanics of learning: Generalization
Manfred Opper · 1995
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The concentration of measure phenomenon
Michel Ledoux · 2001
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Learning to generalize
Manfred Opper · 2001
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Imagenet: A large-scale hierarchical image database
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei · 2009
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Learning multiple layers of features from tiny images
Alex Krizhevsky, Geoffrey Hinton, et al · 2009
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Very deep convolutional networks for large-scale image recognition
Karen Simonyan and Andrew Zisserman · 2014
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Distilling the knowledge in a neural network
Geoffrey Hinton, Oriol Vinyals, and Jeff Dean · 2015
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Sergey Zagoruyko and Nikos Komodakis · 2016
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Sharp minima can generalize for deep nets
Laurent Dinh, Razvan Pascanu, Samy Bengio, and Yoshua Bengio · 2017
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Densely connected convolutional networks
Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kilian Q Weinberger · 2017
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Visualizing the loss landscape of neural nets
Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein · 2017
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mixup: Beyond empirical risk minimization
Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz · 2017
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Empirical study of the topology and geometry of deep networks
Alhussein Fawzi, Seyed-Mohsen Moosavi-Dezfooli, Pascal Frossard, and Stefano Soatto · 2018
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Decision boundary analysis of adversarial examples
Warren He, Bo Li, and Dawn Song · 2018
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A modern take on the bias-variance tradeoff in neural networks
Brady Neal, Sarthak Mittal, Aristide Baratin, Vinayak Tantia, Matthew Scicluna, Simon Lacoste-Julien, and Ioannis Mitliagkas · 2018
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Are adversarial examples inevitable?
Ali Shafahi, W Ronny Huang, Christoph Studer, Soheil Feizi, and Tom Goldstein · 2018
High-dimensional dynamics of generalization error in neural networks
Madhu S Advani, Andrew M Saxe, and Haim Sompolinsky · 2020
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An image is worth 16x16 words: Transformers for image recognition at scale
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al · 2020
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Double trouble in double descent: Bias and variance (s) in the lazy regime
Stéphane d’Ascoli, Maria Refinetti, Giulio Biroli, and Florent Krzakala · 2020
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Sharpness-aware minimization for efficiently improving generalization
Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur · 2020
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Adversarially robust distillation
Micah Goldblum, Liam Fowl, Soheil Feizi, and Tom Goldstein · 2020
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A jamming transition from under-to over-parametrization affects loss landscape and generalization
Stefano Spigler, Mario Geiger, Stéphane d’Ascoli, Levent Sagun, Giulio Biroli, and Matthieu Wyart · 2018
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Reconciling modern machine-learning practice and the classical bias–variance trade-off
Mikhail Belkin, Daniel Hsu, Siyuan Ma, and Soumik Mandal · 2019
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Entropy-sgd: Biasing gradient descent into wide valleys
Pratik Chaudhari, Anna Choromanska, Stefano Soatto, Yann LeCun, Carlo Baldassi, Christian Borgs, Jennifer Chayes, Levent Sagun, and Riccardo Zecchina · 2019
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Surprises in high-dimensional ridgeless least squares interpolation
Trevor Hastie, Andrea Montanari, Saharon Rosset, and Ryan J Tibshirani · 2019
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Characterizing the decision boundary of deep neural networks
Hamid Karimi, Tyler Derr, and Jiliang Tang · 2019
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Deep double descent: Where bigger models and more data hurt
Preetum Nakkiran, Gal Kaplun, Yamini Bansal, Tristan Yang, Boaz Barak, and Ilya Sutskever · 2019
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Pytorch image models
Ross Wightman · 2019
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Harmless interpolation of noisy data in regression
Vidya Muthukumar, Kailas Vodrahalli, Vignesh Subramanian, and Anant Sahai · 2020
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Rethinking bias-variance trade-off for generalization of neural networks
Zitong Yang, Yaodong Yu, Chong You, Jacob Steinhardt, and Yi Ma · 2020
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Yehuda Dar, Vidya Muthukumar, and Richard G Baraniuk · 2021
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Stochastic training is not necessary for generalization
Jonas Geiping, Micah Goldblum, Phillip E Pope, Michael Moeller, and Tom Goldstein · 2021
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Does knowledge distillation really work?
Samuel Stanton, Pavel Izmailov, Polina Kirichenko, Alexander A Alemi, and Andrew Gordon Wilson · 2021
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Mlp-mixer: An all-mlp architecture for vision
Ilya Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszkoreit, et al · 2021
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Understanding deep learning (still) requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2021
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Decision boundary variability and generalization in neural networks
Anonymous · 2022
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