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Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with $100\%$ accuracy.
Approximation by superpositions of a sigmoidal function
Cybenko, G · 1989
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Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., and White, H · 1989
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Universal approximation bounds for superpositions of a sigmoidal function
Barron, A. R · 1993
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
Leshno, M., Lin, V. Y., Pinkus, A., and Schocken, S · 1993
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Consistency of the k-nearest neighbor rule
Devroye, L., Györfi, L., and Lugosi, G · 1996
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Harmonic analysis of neural networks
Candès, E. J · 1999
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A note on the universal approximation capability of support vector machines
Hammer, B. and Gersmann, K · 2003
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Gaussian processes in machine learning
Rasmussen, C. E · 2004
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Model selection in kernel methods based on a spectral analysis of label information
Braun, M. L., Lange, T., and Buhmann, J. M · 2006
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Learning deep architectures for ai
Bengio, Y. et al · 2009
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Positive definite kernels: past, present and future
Fasshauer, G. E · 2011
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Explaining and harnessing adversarial examples
Goodfellow, I. J., Shlens, J., and Szegedy, C · 2014
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
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On the number of linear regions of deep neural networks
Montufar, G. F., Pascanu, R., Cho, K., and Bengio, Y · 2014
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In search of the real inductive bias: On the role of implicit regularization in deep learning
Neyshabur, B., Tomioka, R., and Srebro, N · 2014
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Fourier transforms of polytopes, solid angle sums, and discrete volume
Diaz, R., Le, Q.-N., and Robins, S · 2016
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The power of depth for feedforward neural networks
Eldan, R. and Shamir, O · 2016
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Deep Learning
Goodfellow, I., Bengio, Y., and Courville, A · 2016
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An automated nudged elastic band method
Fourier series, Fourier transform and their applications to mathematical physics
Serov, V · 2017
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Neural network with unbounded activation functions is universal approximator
Sonoda, S. and Murata, N · 2017
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The implicit bias of gradient descent on separable data
Soudry, D., Hoffer, E., Nacson, M. S., Gunasekar, S., and Srebro, N · 2017
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Understanding deep neural networks with rectified linear units
Arora, R., Basu, A., Mianjy, P., and Mukherjee, A · 2018
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Essentially no barriers in neural network energy landscape
Draxler, F., Veschgini, K., Salmhofer, M., and Hamprecht, F. A · 2018
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Kolsbjerg, E. L., Groves, M. N., and Hammer, B · 2016
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Exponential expressivity in deep neural networks through transient chaos
Poole, B., Lahiri, S., Raghu, M., Sohl-Dickstein, J., and Ganguli, S · 2016
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On the expressive power of deep neural networks
Raghu, M., Poole, B., Kleinberg, J., Ganguli, S., and Sohl-Dickstein, J · 2016
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Benefits of depth in neural networks
Telgarsky, M · 2016
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A closer look at memorization in deep networks
Arpit, D., Jastrzebski, S., Ballas, N., Krueger, D., Bengio, E., Kanwal, M. S., Maharaj, T., Fischer, A., Courville, A., Bengio, Y., et al · 2017
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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
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Diving into the shallows: a computational perspective on large-scale shallow learning
Ma, S. and Belkin, M · 2017
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Spectral normalization for generative adversarial networks
Miyato, T., Kataoka, T., Koyama, M., and Yoshida, Y · 2018
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Sensitivity and generalization in neural networks: an empirical study
Novak, R., Bahri, Y., Abolafia, D. A., Pennington, J., and Sohl-Dickstein, J · 2018
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Theory of deep learning iii: the non-overfitting puzzle
Poggio, T., Kawaguchi, K., Liao, Q., Miranda, B., Rosasco, L., Boix, X., Hidary, J., and Mhaskar, H · 2018
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Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus
Spivak, M · 2018
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Understanding training and generalization in deep learning by fourier analysis
Xu, Z. J · 2018
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Training behavior of deep neural network in frequency domain
Xu, Z.-Q. J., Zhang, Y., and Xiao, Y · 2018
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Tropical geometry of deep neural networks
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