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We combine Riemannian geometry with the mean field theory of high dimensional chaos to study the nature of signal propagation in generic, deep neural networks with random weights.
Chaos in random neural networks
Haim Sompolinsky, A Crisanti, and HJ Sommers · 1988
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Riemannian manifolds: an introduction to curvature , volume 176
John M Lee · 2006
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Untangling invariant object recognition
James J DiCarlo and David D Cox · 2007
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Shallow vs. deep sum-product networks
Olivier Delalleau and Yoshua Bengio · 2011
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Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton · 2012
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Playing atari with deep reinforcement learning
Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, and Martin Riedmiller · 2013
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Representation learning: A review and new perspectives
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On the number of linear regions of deep neural networks
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Chris Piech, Jonathan Bassen, Jonathan Huang, Surya Ganguli, Mehran Sahami, Leonidas J Guibas, and Jascha Sohl-Dickstein · 2015
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The power of depth for feedforward neural networks
Ronen Eldan and Ohad Shamir · 2015
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Representation benefits of deep feedforward networks
Matus Telgarsky · 2015
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Learning real and boolean functions: When is deep better than shallow
Hrushikesh Mhaskar, Qianli Liao, and Tomaso Poggio · 2016
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On the expressive power of deep neural networks
Maithra Raghu, Ben Poole, Jon Kleinberg, Surya Ganguli, and Jascha Sohl-Dickstein · 2016
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