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In our work, we bridge deep neural network design with numerical differential equations.
The modified equation to the stability and accuracy analysis of finite-difference methods
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Geometric level set methods in imaging, vision, and graphics
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Tony F. Chan and Jianhong Shen · 2005
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Mathematical problems in image processing: partial differential equations and the calculus of variations , volume 147
Gilles Aubert and Pierre Kornprobst · 2006
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Yoshua Bengio · 2009
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Learning fast approximations of sparse coding
Karol Gregor and Yann LeCun · 2010
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Learning pdes for image restoration via optimal control
Risheng Liu, Zhouchen Lin, Wei Zhang, and Zhixun Su · 2010
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Optimization and dynamical systems
Uwe Helmke and John B Moore · 2012
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Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton · 2012
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An introduction to stochastic differential equations
Lawrence C Evans · 2013
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Toward designing intelligent pdes for computer vision: An optimal control approach
Risheng Liu, Zhouchen Lin, Wei Zhang, Kewei Tang, and Zhixun Su · 2013
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Imagenet large scale visual recognition challenge
Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, and Michael Bernstein · 2014
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Very deep convolutional networks for large-scale image recognition
Karen Simonyan and Andrew Zisserman · 2014
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On learning optimized reaction diffusion processes for effective image restoration
Yunjin Chen, Wei Yu, and Thomas Pock · 2015
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Variational dropout and the local reparameterization trick
Diederik P. Kingma, Tim Salimans, and Max Welling · 2015
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Deeply-supervised nets
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Five ways to avoid storing source wavefield snapshots in 2d elastic prestack reverse time migration
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A differential equation for modeling nesterov’s accelerated gradient method: theory and insights
Reversible architectures for arbitrarily deep residual neural networks
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A proposal on machine learning via dynamical systems
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