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We provide several new depth-based separation results for feed-forward neural networks, proving that various types of simple and natural functions can be better approximated using deeper networks than shallower ones, even if the shallower networks are much larger.
Approximation by superpositions of a sigmoidal function
Cybenko, George · 1989
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Approximation capabilities of multilayer feedforward networks
Hornik, Kurt · 1991
Earlier work this paper cites.
Shallow vs. deep sum-product networks
Delalleau, O. and Bengio, Y · 2011
Earlier work this paper cites.
On the complexity of shallow and deep neural network classifiers
Bianchini, M. and Scarselli, F · 2014
Earlier work this paper cites.
On the expressive efficiency of sum product networks
Martens, J. and Medabalimi, V · 2014
Earlier work this paper cites.
Deep residual learning for image recognition
He, Kaiming, Zhang, Xiangyu, Ren, Shaoqing, and Sun, Jian · 2015
Cited alongside, same era.
On the expressive power of deep learning: A tensor analysis
Cohen, Nadav, Sharir, Or, and Shashua, Amnon · 2016
Cited alongside, same era.
The power of depth for feedforward neural networks
Eldan, Ronen and Shamir, Ohad · 2016
Cited alongside, same era.
Liang, Shiyu and Srikant, R · 2016
Cited alongside, same era.
Why and when can deep–but not shallow–networks avoid the curse of dimensionality: a review
Poggio, Tomaso, Mhaskar, Hrushikesh, Rosasco, Lorenzo, Miranda, Brando, and Liao, Qianli · 2016
Cited alongside, same era.
Exponential expressivity in deep neural networks through transient chaos
Poole, Ben, Lahiri, Subhaneil, Raghu, Maithreyi, Sohl-Dickstein, Jascha, and Ganguli, Surya · 2016
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Provable approximation properties for deep neural networks
Shaham, Uri, Cloninger, Alexander, and Coifman, Ronald R · 2016
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Benefits of depth in neural networks
Telgarsky, Matus · 2016
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Error bounds for approximations with deep relu networks
Yarotsky, Dmitry · 2016
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