NumDNN.bib

@article{lecun2015deep,
  title={Deep learning},
  author={LeCun, Yann and Bengio, Yoshua and Hinton, Geoffrey},
  journal={Nature},
  volume={521},
  number={7553},
  pages={436--444},
  year={2015},
  publisher={Nature Research}
}
@inproceedings{LeCun1990,
author = {LeCun, Y and Boser, B E and Denker, J S},
title = {{Handwritten digit recognition with a back-propagation network}},
booktitle = {Advances in neural information processing systems},
year = {1990},
pages = {396--404}
}


@article{Rosenblatt1958,
author = {Rosenblatt, F},
title = {{The perceptron: A probabilistic model for information storage and organization in the brain.}},
journal = {Psychological review},
year = {1958},
volume = {65},
number = {6},
pages = {386--408},
publisher = {American Psychological Association},
doi = {10.1037/h0042519},
url = {http://psycnet.apa.org/journals/rev/65/6/386.html}
}
@article{Rumelhart1986,
  title={Learning representations by back-propagating errors},
  author={Rumelhart, D.E. and Hinton, Geoffrey and Williams, R,J.},
  journal={Nature},
  volume={323},
  number={6088},
  pages={533--538},
  year={1986}
}

@article{bengio2009learning,
  title={Learning deep architectures for {AI}},
  author={Bengio, Yoshua and others},
  journal={Foundations and trends{\textregistered} in Machine Learning},
  volume={2},
  number={1},
  pages={1--127},
  year={2009},
  publisher={Now Publishers, Inc.}
}

@article{KrizhevskySutskeverHinton2012,
	Author = {A. Krizhevsky and I. Sutskever and G. Hinton},
	Journal = {Advances in neural information processing systems},
	Title = { Imagenet classification with deep convolutional neural networks},
    Volume = {61},
    pages = {1097–1105},
	Year = {2012}
}

@article{CollobertEtAl2011,
author = {Collobert, Ronan and Weston, Jason and Bottou, L{\'e}on and Karlen, Michael and Kavukcuoglu, Koray and Kuksa, Pavel},
title = {{Natural Language Processing (Almost) from Scratch}},
journal = {Journal of Machine Learning Research},
year = {2011},
volume = {12},
pages = {2493--2537},
url = {http://www.jmlr.org/papers/v12/collobert11a.html}
}


@article{BordesEtAl2014,
author = {Bordes, Antoine and Chopra, Sumit and Weston, Jason},
title = {{Question Answering with Subgraph Embeddings}},
journal = {arXiv preprint arXiv:1406.3676},
year = {2014},
eprint = {1406.3676v3},
eprinttype = {arxiv},
eprintclass = {cs.CL},
url = {http://arxiv.org/abs/1406.3676v3}
}

@article{JeanEtAl2014,
author = {Jean, S{\'e}bastien and Cho, Kyunghyun and Memisevic, Roland and Bengio, Yoshua},
title = {{On Using Very Large Target Vocabulary for Neural Machine Translation}},
journal = {arXiv preprint arXiv:1412.2007},
year = {2014},
eprint = {1412.2007v2},
eprinttype = {arxiv},
eprintclass = {cs.CL},
url = {http://arxiv.org/abs/1412.2007v2}
}


@inproceedings{RainaEtAl2009,
author = {Raina, Rajat and Madhavan, Anand and Ng, Andrew Y},
title = {{Large-scale deep unsupervised learning using graphics processors}},
booktitle = {the 26th Annual International Conference},
year = {2009},
pages = {873--880},
publisher = {ACM},
month = jun,
doi = {10.1145/1553374.1553486},
url = {http://portal.acm.org/citation.cfm?doid=1553374.1553486}
}

@article{hinton2012deep,
  title={Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups},
  author={Hinton, Geoffrey and Deng, Li and Yu, Dong and Dahl, George E and Mohamed, Abdel-rahman and Jaitly, Navdeep and Senior, Andrew and Vanhoucke, Vincent and Nguyen, Patrick and Sainath, Tara N and others},
  journal={IEEE Signal Processing Magazine},
  volume={29},
  number={6},
  pages={82--97},
  year={2012},
  publisher={IEEE}
}


@booklet{AscherGreif2011,
title = {{A First Course on Numerical Methods}},
author = {Ascher, U M and Greif, C},
howpublished = {SIAM},
address = {Philadelphia},
year = {2011}
}

@book{NocedalWright2006,
author = {Nocedal, Jorge and Wright, Stephen},
title = {{Numerical Optimization}},
publisher = {Springer Science {\&} Business Media},
year = {2006},
series = {Springer Series in Operations Research and Financial Engineering},
address = {New York},
month = dec
}

@book{Saad2003,
author = {Saad, Yousef},
title = {{Iterative Methods for Sparse Linear Systems}},
publisher = {SIAM},
year = {2003},
series = {Second Edition},
address = {Philadelphia},
month = apr
}

@book{Vogel2002,
author = {Vogel, Curtis R},
title = {{Computational Methods for Inverse Problems}},
publisher = {SIAM},
year = {2002},
address = {Philadelphia}
}


@book{Hansen2010,
author = {Hansen, Per Christian},
title = {{Discrete inverse problems}},
publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA},
year = {2010},
volume = {7},
series = {Fundamentals of Algorithms}
}

@book{Hansen1998,
author = {Hansen, Per Christian},
title = {{Rank-deficient and discrete ill-posed problems}},
publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA},
year = {1998},
series = {SIAM Monographs on Mathematical Modeling and Computation}
}


@book{BoydVandenberghe2004,
author = {Boyd, Stephen P and Vandenberghe, Lieven},
title = {{Convex Optimization}},
publisher = {Cambridge University Press},
year = {2004},
month = mar
}


@book{Beck2014,
author = {Beck, Amir},
title = {{Introduction to Nonlinear Optimization}},
publisher = {SIAM},
year = {2014},
series = {Theory, Algorithms, and Applications with MATLAB},
address = {Philadelphia},
month = oct
}

@article{Cybenko1989,
author = {Cybenko, G},
title = {{Approximation by superpositions of a sigmoidal function}},
journal = {Mathematics of Control, Signals and Systems},
year = {1989},
volume = {2},
number = {4},
pages = {303--314}
}


@article{HornikEtAl1989,
author = {Hornik, K and Stinchcombe, M and White, H},
title = {{Multilayer feedforward networks are universal approximators}},
journal = {Neural Networks},
year = {1989},
volume = {2},
number = {5},
pages = {359--366}
}

@article{HuangEtAl2006,
author = {Huang, Guang-Bin and Zhu, Qin-Yu and Siew, Chee-Kheong},
title = {{Extreme learning machine: Theory and applications}},
journal = {Neurocomputing},
year = {2006},
volume = {70},
number = {1-3},
pages = {489--501},
month = dec
}


@article{bliss1919,
  title={The use of adjoint systems in the problem of differential corrections for trajectories},
  author={Bliss, Go A},
  journal={JUS Artillery},
  volume={51},
  pages={296--311},
  year={1919}
}

@book{BorzSchulz2012,
author = {Borz{\`\i}, Alfio and Schulz, Volker},
title = {{Computational optimization of systems governed by partial differential equations}},
publisher = {SIAM, Philadelphia, PA},
year = {2012},
volume = {8},
keywords = {PDE-ConstrainedOpti},
isbn = {978-1-611972-04-7},
url = {http://www.ams.org/mathscinet-getitem?mr=MR2895881}		
}


@article{LiEtAl2017,
author = {Li, Hao and Xu, Zheng and Taylor, Gavin and Goldstein, Tom},
title = {{Visualizing the Loss Landscape of Neural Nets}},
year = {2017},
eprint = {1712.09913},
eprinttype = {arxiv}
}

@article{E2017,
author = {E, Weinan},
title = {{A Proposal on Machine Learning via Dynamical Systems}},
journal = {Communications in Mathematics and Statistics},
year = {2017},
volume = {5},
number = {1},
pages = {1--11},
month = mar
}
@article{HaberRuthotto2017,
  author    = {Eldad Haber and
               Lars Ruthotto},
journal     = {Inverse Problems},
  title     = {Stable Architectures for Deep Neural Networks},
  volume    = {34},
  issue     = {1},
  year      = {2017},
pages      = {014004},
  url       = {http://arxiv.org/abs/1705.03341}
}
@inproceedings{he2016deep,
  title={Deep residual learning for image recognition},
  author={He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
  booktitle={Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition},
  pages={770--778},
  year={2016}
}


@inproceedings{he2016identity,
  title={Identity mappings in deep residual networks},
  author={He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
  booktitle={European Conference on Computer Vision},
  pages={630--645},
  year={2016},
  organization={Springer}
}


@book{Ascher2010,
	Address = {Philadelphia},
	Author = {U.M. Ascher},
	Publisher = {SIAM},
	Title = {Numerical methods for Evolutionary Differential Equations},
	Year = {2010}}
@book{AscherPetzold1998,
	Address = {Philadelphia, PA},
	Author = {U. Ascher and L. Petzold},
	Publisher = {SIAM},
	Title = {Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations},
	Year = 1998}

@article{bottou2016optimization,
author = {Bottou, L{\'e}on and Curtis, Frank E and Nocedal, Jorge},
title = {{Optimization Methods for Large-Scale Machine Learning}},
journal = {arXiv preprint [stat.ML] (1606.04838v1)},
year = {2016}
}

@article{RobbinsMonro1951,
author = {Robbins, H and Monro, S},
title = {{A Stochastic Approximation Method}},
journal = {The annals of mathematical statistics},
year = {1951},
volume = {22},
number = {3},
pages = {400--407}
}


@book{HansenNagyOLeary2006,
author = {Hansen, P C and Nagy, J G and O'Leary, D P},
title = {{Deblurring Images: Matrices, Spectra and Filtering}},
publisher = {Society for Industrial and Applied Mathematics (SIAM)},
year = {2006},
series = {Matrices, Spectra, and Filtering},
address = {Philadelphia, PA}
}


@article{GoPe03,
	Author = {G.~Golub and V.~Pereyra},
	Journal = {Inverse Problems},
	Pages = {R1--R26},
	Title = {Separable nonlinear least squares: the variable projection method and its applications},
	Volume = 19,
	Year = 2003}
	
@article{GoPe1973,
author = {Golub, G H and Pereyra, V},
title = {{The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate}},
journal = {SIAM Journal on Numerical Analysis},
year = {1973},
volume = {10},
number = {2},
pages = {413--432}
}

@article{OLearyRust2013,
author = {O'Leary, Dianne P and Rust, Bert W},
title = {{Variable projection for nonlinear least squares problems}},
journal = {Computational Optimization and Applications. An International Journal},
year = {2013},
volume = {54},
number = {3},
pages = {579--593}
}

@article{IoffeSzegedy2015,
author = {Ioffe, Sergey and Szegedy, Christian},
title = {{Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift}},
journal = {arXiv preprint [cs.LG] 1502.03167v3},
year = {2015}
}

@article{RudinOsherFatemi1992,
author = {Rudin, Leonid I and Osher, Stanley and Fatemi, Emad},
title = {{Nonlinear total variation based noise removal algorithms}},
journal = {Physica D: Nonlinear Phenomena},
year = {1992},
volume = {60},
number = {1-4},
pages = {259--268}
}

@article{UlyanovEtAl2016,
author = {Ulyanov, Dmitry and Vedaldi, Andrea and Lempitsky, Victor},
title = {{Instance Normalization: The Missing Ingredient for Fast Stylization}},
journal = {arxiv preprint [cs.CV] 1607.08022v3},
year = {2016}
}

@article{ChenPock2017,
author = {Chen, Yunjin and Pock, Thomas},
title = {{Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration.}},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
year = {2017},
volume = {39},
number = {6},
pages = {1256--1272},
month = jun
}

@article{Bertsekas2015,
author = {Bertsekas, Dimitri P},
title = {{Incremental Gradient, Subgradient, and Proximal Methods for Convex Optimization: A Survey}},
journal = {arXiv preprint [cs.SY 1507.01030v1] },
year = {2015}
}


@article{Bottou2012,
author = {Bottou, L},
title = {{Stochastic gradient descent tricks}},
journal = {Neural networks: Tricks of the trade},
year = {2012}
}


@article{Mathieu:2013wa,
author = {Mathieu, Michael and Henaff, Mikael and LeCun, Yann},
title = {{Fast Training of Convolutional Networks through FFTs}},
year = {2013},
journal = {arxiv preprint 1312.5851}
}

@article{Vasilache:2014wh,
author = {Vasilache, Nicolas and Johnson, Jeff and Mathieu, Michael and Chintala, Soumith and Piantino, Serkan and LeCun, Yann},
title = {{Fast Convolutional Nets With fbfft: A GPU Performance Evaluation}},
journal = {arxiv preprint [cs.LG] 1412.7580v3},
year = {2014}
}