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It is well-known that neural networks are computationally hard to train.
Relations among complexity measures
N. Pippenger and M. Fischer · 1979
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Training a 3-node neural network is np-complete
A. Blum and R. Rivest · 1992
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Exponentially many local minima for single neurons
P. Auer, M. Herbster, and M. Warmuth · 1996
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Neural Network Learning - Theoretical Foundations
M. Anthony and P. Bartlett · 2002
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Hardness results for neural network approximation problems
P. L. Bartlett and S. Ben-David · 2002
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Histograms of oriented gradients for human detection
N. Dalal and B. Triggs · 2005
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Cryptographic hardness for learning intersections of halfspaces
A. Klivans and A. Sherstov · 2006
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Introduction to the Theory of Computation
M. Sipser · 2006
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Agnostically learning halfspaces
A. Kalai, A. Klivans, Y. Mansour, and R. Servedio · 2008
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Learning and smoothed analysis
A. Kalai, A. Samorodnitsky, and S.-H. Teng · 2009
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Polynomial regression under arbitrary product distributions
E. Blais, R. O’Donnell, and K. Wimmer · 2010
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Large-scale convex minimization with a low-rank constraint
S. Shalev-Shwartz, A. Gonen, and O. Shamir · 2011
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Learning kernel-based halfspaces with the 0-1 loss
S. Shalev-Shwartz, O. Shamir, and K. Sridharan · 2011
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Imagenet classification with deep convolutional neural networks
A. Krizhevsky, I. Sutskever, and G. Hinton · 2012
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Representation learning: A review and new perspectives
Y. Bengio, A. Courville, and P. Vincent · 2013
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Improving deep neural networks for lvcsr using rectified linear units and dropout
G. Dahl, T. Sainath, and G. Hinton · 2013
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On the importance of initialization and momentum in deep learning
I. Sutskever, J. Martens, G. Dahl, and G. Hinton · 2013
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Visualizing and understanding convolutional neural networks
M. Zeiler and R. Fergus · 2013
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Learning polynomials with neural networks
A. Andoni, R. Panigrahy, G. Valiant, and L. Zhang · 2014
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Learning sparse polynomial functions
A. Andoni, R. Panigrahy, G. Valiant, and L. Zhang · 2014
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Provable bounds for learning some deep representations
S. Arora, A. Bhaskara, R. Ge, and T. Ma · 2013
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From average case complexity to improper learning complexity
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