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Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes.
Approximation by superpositions of a sigmoidal function
Cybenko, G · 1989
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Universal approximation bounds for superpositions of a sigmoidal function
Barron, A. R · 1993
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Approximation and estimation bounds for artificial neural networks
Barron, A. R · 1994
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Density in approximation theory
Pinkus, A · 2005
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Introduction to Nonparametric Estimation
Tsybakov, A. B · 2008
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ImageNet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., and Hinton, G. E · 2012
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Approximating multivariable functions by feedforward neural nets
Kainen, P. C., Kůrková, V., and Sanguineti, M · 2013
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Predicting the sequence specificities of DNA-and RNA-binding proteins by deep learning
Alipanahi, B., Delong, A., Weirauch, M. T., and Frey, B. J · 2015
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Mathematical foundations of infinite-dimensional statistical models , volume 40
Giné, E. and Nickl, R · 2015
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Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification
He, K., Zhang, X., Ren, S., and Sun, J · 2015
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
Ioffe, S. and Szegedy, C · 2015
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U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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Going deeper with convolutions
Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V., and Rabinovich, A · 2015
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Predicting effects of noncoding variants with deep learning-based sequence model
Zhou, J. and Troyanskaya, O. G · 2015
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Deep residual learning for image recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
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Understanding and improving convolutional neural networks via concatenated rectified linear units
Shang, W., Sohn, K., Almeida, D., and Lee, H · 2016
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Google’s neural machine translation system: Bridging the gap between human and machine translation
Wu, Y., Schuster, M., Chen, Z., Le, Q. V., Norouzi, M., Macherey, W., Krikun, M., Cao, Y., Gao, Q., Macherey, K., et al · 2016
Cited alongside, same era.
Densely connected convolutional networks
Huang, G., Liu, Z., Van Der Maaten, L., and Weinberger, K. Q · 2017
Cited alongside, same era.
On the ability of neural nets to express distributions
Lee, H., Ge, R., Ma, T., Risteski, A., and Arora, S · 2017
Cited alongside, same era.
Approximation by combinations of ReLU and squared ReLU ridge functions with ℓ 1 \ell_{1} and ℓ 0 \ell_{0} controls
Klusowski, J. M. and Barron, A. R · 2018
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ResNet with one-neuron hidden layers is a universal approximator
Lin, H. and Jegelka, S · 2018
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Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations
Lu, Y., Zhong, A., Li, Q., and Dong, B · 2018
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Spectral normalization for generative adversarial networks
Miyato, T., Kataoka, T., Koyama, M., and Yoshida, Y · 2018
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Functional gradient boosting based on residual network perception
Nitanda, A. and Suzuki, T · 2018
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The universal approximation power of finite-width deep ReLU networks
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Lu, Z., Pu, H., Wang, F., Hu, Z., and Wang, L · 2017
Cited alongside, same era.
Nonparametric regression using deep neural networks with ReLU activation function
Schmidt-Hieber, J · 2017
Cited alongside, same era.
Error bounds for approximations with deep ReLU networks
Yarotsky, D · 2017
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Stronger generalization bounds for deep nets via a compression approach
Arora, S., Ge, R., Neyshabur, B., and Zhang, Y · 2018
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Dynamical isometry and a mean field theory of RNNs: Gating enables signal propagation in recurrent neural networks
Chen, M., Pennington, J., and Schoenholz, S · 2018
Cited alongside, same era.
Spherical CNNs
Cohen, T. S., Geiger, M., Köhler, J., and Welling, M · 2018
Cited alongside, same era.
Universal approximation by a slim network with sparse shortcut connections
Fan, F., Wang, D., and Wang, G · 2018
Cited alongside, same era.
Perekrestenko, D., Grohs, P., Elbrächter, D., and Bölcskei, H · 2018
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Fast generalization error bound of deep learning from a kernel perspective
Suzuki, T · 2018
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Universal approximations of invariant maps by neural networks
Yarotsky, D · 2018
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Universality of deep convolutional neural networks
Zhou, D.-X · 2018
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Understanding generalization and optimization performance of deep CNNs
Zhou, P. and Feng, J · 2018
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Optimal approximation with sparsely connected deep neural networks
Bölcskei, H., Grohs, P., Kutyniok, G., and Petersen, P · 2019
Closest in time.
Deep neural networks learn non-smooth functions effectively
Imaizumi, M. and Fukumizu, K · 2019
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Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality
Suzuki, T · 2019
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