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It is well-known that modern neural networks are vulnerable to adversarial examples.
Adversarial robustness may be at odds with simplicity
Nakkiran, P · 1901
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Liii. on lines and planes of closest fit to systems of points in space
Pearson, K · 1901
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Adversarial training can hurt generalization
Raghunathan, A · 1906
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A relation between volume, mean curvature and diameter
Bishop, R. L · 1964
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On the capabilities of multilayer perceptrons
Baum, E. B · 1988
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Approximation by superpositions of a sigmoidal function
Cybenko, G · 1989
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Optimal nonlinear approximation
DeVore, R. A · 1989
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Approximation capabilities of multilayer feedforward networks
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Boser, B. E · 1992
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Polynomial bounds for vc dimension of sigmoidal neural networks
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Anthony, M · 1999
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Nonlinear dimensionality reduction by locally linear embedding
Roweis, S. T · 2000
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A global geometric framework for nonlinear dimensionality reduction
Tenenbaum, J. B · 2000
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Network size and weights size for memorization with two-layers neural networks
Bubeck, S · 2006
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Visualizing data using t-sne journal of machine learning research
Hinton, G · 2008
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Finding the homology of submanifolds with high confidence from random samples
Niyogi, P · 2008
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Random projections of smooth manifolds
Baraniuk, R. G · 2009
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Evasion attacks against machine learning at test time
Biggio, B · 2013
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Intriguing properties of neural networks
Szegedy, C · 2013
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Explaining and harnessing adversarial examples
Goodfellow, I. J · 2014
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Benefits of depth in neural networks
Telgarsky, M · 2016
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Auto-encoder based dimensionality reduction
Wang, Y · 2016
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Why deep neural networks for function approximation?
Liang, S · 2017
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The expressive power of neural networks: A view from the width
Lu, Z · 2017
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Towards deep learning models resistant to adversarial attacks
Madry, A · 2017
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Exploring generalization in deep learning
Neyshabur, B · 2017
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Neural networks and rational functions
Telgarsky, M · 2017
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Error bounds for approximations with deep relu networks
Yarotsky, D · 2017
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Convergence of adversarial training in overparametrized neural networks
Gao, R · 2019
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On the intrinsic dimensionality of image representations
Gong, S · 2019
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Universal function approximation by deep neural nets with bounded width and relu activations
Hanin, B · 2019
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Adversarial training for free!
Shafahi, A · 2019
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Robustness may be at odds with accuracy
Tsipras, D · 2019
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Small relu networks are powerful memorizers: a tight analysis of memorization capacity
Yun, C · 2019
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Zhang, C · 2017
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Deep nets for local manifold learning
Chui, C. K · 2018
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Bert: Pre-training of deep bidirectional transformers for language understanding
Devlin, J · 2018
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Foundations of machine learning
Mohri, M · 2018
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Adversarially robust generalization requires more data
Schmidt, L · 2018
Cited alongside, same era.
Are adversarial examples inevitable?
Shafahi, A · 2018
Cited alongside, same era.
Theoretically principled trade-off between robustness and accuracy
Zhang, H · 2019
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Sharp statistical guaratees for adversarially robust gaussian classification
Dan, C · 2020
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Overfitting in adversarially robust deep learning
Rice, L · 2020
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A closer look at accuracy vs. robustness
Yang, Y.-Y · 2020
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Sample complexity of robust linear classification on separated data
Bhattacharjee, R · 2021
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A law of robustness for two-layers neural networks
Bubeck, S · 2021
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A universal law of robustness via isoperimetry
Bubeck, S · 2021
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Highly accurate protein structure prediction with alphafold
Jumper, J · 2021
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Relative flatness and generalization
Petzka, H · 2021
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An exponential improvement on the memorization capacity of deep threshold networks
Rajput, S · 2021
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On the optimal memorization power of relu neural networks
Vardi, G · 2021
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Hassani, H · 2022
Closest in time.
Liu, H · 2022
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Optimal approximation rate of relu networks in terms of width and depth
Shen, Z · 2022
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How many data are needed for robust learning?
Zhang, H · 2022
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