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In the recent literature the important role of depth in deep learning has been emphasized.
Mathematical analysis
Apostol, T. M · 1974
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Cybenko, G · 1989
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Multilayer feedforward networks are universal approximators
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
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Shallow vs. deep sum-product networks
Delalleau, O. and Bengio, Y · 2011
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Sum-product networks: A new deep architecture
Poon, H. and Domingos, P · 2011
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Rectifier nonlinearities improve neural network acoustic models
Maas, A. L., Hannun, A. Y., and Ng, A. Y · 2013
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Caffe: Convolutional architecture for fast feature embedding
Jia, Y., Shelhamer, E., Donahue, J., Karayev, S., Long, J., Grishick, R., Guadarrama, S., and Darrell, T · 2014
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On the number of linear regions of deep neural networks
Montufar, G., Pascanu, R., Cho, K., and Bengio, Y · 2014
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On the number of response regions of deep feedforward networks with piecewise linear activations
Pascanu, R., Montufar, G., and Bengio, Y · 2014
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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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Representation benefits of deep feedforward networks, 2015
Telgarsky, M · 2015
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Fast and accurate deep network learning by exponential linear units (elus)
Clevert, D., Unterthiner, T., and Hochreiter, S · 2016
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Convolutional rectifier networks as generalized tensor decompositions
Cohen, N. and Shashua, A · 2016
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On the expressive power of deep learning: A tensor analysis
Cohen, N., Sharir, O., and Shashua, A · 2016
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The power of depth for feedforward neural networks
Classification regions of deep neural networks, 2017
Fawzi, A., Dezfooli, S. M. M., Frossard, P., and Soatto, S · 2017
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Approximating continuous functions by relu nets of minimal width, 2017
Hanin, B. and Sellke, M · 2017
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Adversarial examples in the physical world
Kurakin, A., Goodfellow, I., and Bengio, S · 2017
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Why deep neural networks for function approximation?
Liang, S. and Srikant, R · 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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The loss surface of deep and wide neural networks
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Eldan, R. and Shamir, O · 2016
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Deep Learning
Goodfellow, I., Bengio, Y., and Courville, A · 2016
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Adversarial machine learning at scale
Kurakin, A., Goodfellow, I., and Bengio, S · 2016
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Deep vs. shallow networks : An approximation theory perspective, 2016
Mhaskar, H. and Poggio, T · 2016
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Why and when can deep – but not shallow – networks avoid the curse of dimensionality: a review, 2016
Poggio, T., Mhaskar, H., Rosasco, L., Miranda, B., and Liao, Q · 2016
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Benefits of depth in neural networks
Telgarsky, M · 2016
Cited alongside, same era.
Error bounds for approximations with deep relu networks, 2016
Yarotsky, D · 2016
Cited alongside, same era.
Nguyen, Q. and Hein, M · 2017
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On the expressive power of deep neural networks
Raghu, M., Poole, B., Kleinberg, J., Ganguli, S., and Sohl-Dickstein, J · 2017
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Depth-width tradeoffs in approximating natural functions with neural networks
Safran, I. and Shamir, O · 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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A tropical approach to neural networks with piecewise linear activations, 2018
Charisopoulos, V. and Maragos, P · 2018
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Optimization landscape and expressivity of deep cnns
Nguyen, Q. and Hein, M · 2018
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Bounding and counting linear regions of deep neural networks, 2018
Serra, T., Tjandraatmadja, C., and Ramalingam, S · 2018
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