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Recent advances in adversarial attacks and Wasserstein GANs have advocated for use of neural networks with restricted Lipschitz constants.
An iterative algorithm for computing the best estimate of an orthogonal matrix
Björck, A. and Bowie, C. (1971) · 1971
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Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · 1989
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Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., and White, H. (1989) · 1989
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Learning Lipschitz functions
Cooper, D. (1995) · 1995
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The upper bound theorem for polytopes: An easy proof of its asymptotic version
Seidel, R. (1995) · 1995
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A Probabilistic Theory of Pattern Recognition
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Optimal Transport: Old and New
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On the number of linear regions of deep neural networks
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Explaining and harnessing adversarial examples
Goodfellow, I., Shlens, J., and Szegedy, C. (2015) · 2015
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Representation benefits of deep feedforward networks
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Benefits of depth in neural networks
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Wasserstein distributional robustness and regularization in statistical learning
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ReLU deep neural networks and linear finite elements
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Limitations of the Lipschitz constant as a defense against adversarial examples
Huster, T., Chiang, C.-Y. J., and Chadha, R. (2018) · 2018
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Spectral normalization for generative adversarial networks
Miyato, T., Kataoka, T., Koyama, M., and Yoshida, Y. (2018) · 2018
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The expressive power of neural networks: A view from the width
Lu, Z., Pu, H., Wang, F., Hu, Z., and Wang, L. (2017) · 2017
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On the expressive power of deep neural networks
Raghu, M., Poole, B., Kleinberg, J., Ganguli, S., and Dickstein, J. (2017) · 2017
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Error bounds for approximations with deep ReLU networks
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Wei, X., Gong, B., Liu, Z., Lu, W., and Wang, L. (2018) · 2018
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Robust Wasserstein profile inference and applications to machine learning
Blanchet, J., Kang, Y., and Murthy, K. (2019) · 2019
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Some theoretical properties of GANs
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