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Theano: A Python framework for fast computation of mathematical expressions

Rami Al-Rfou, Guillaume Alain, Amjad Almahairi, Christof Angermueller, Dzmitry Bahdanau, Nicolas Ballas, Frederic Bastien, Justin Bayer, Anatoly Belikov, Alexander Belopolsky, Yoshua Bengio, Arnaud Bergeron, James Bergstra, Valentin Bisson, Josh Bleecher Snyder, Nicolas Bouchard, Nicolas Boulanger-Lewandowski, Xavier Bouthillier, Alexandre de Brebisson, Olivier Breuleux, Pierre-Luc Carrier, Kyunghyun Cho, Jan Chorowski, Paul Christiano, Tim Cooijmans, Marc-Alexandre Cote, Myriam Cote, Aaron Courville, Yann N. Dauphin, Olivier Delalleau, Julien Demouth, Guillaume Desjardins, Sander Dieleman, Laurent Dinh, Melanie Ducoffe, Vincent Dumoulin, Samira Ebrahimi Kahou, Dumitru Erhan, Ziye Fan, Orhan Firat, Mathieu Germain, Xavier Glorot, Ian Goodfellow, Matt Graham, Caglar Gulcehre, Philippe Hamel, Iban Harlouchet, Jean-Philippe Heng, Balazs Hidasi, Sina Honari, Arjun Jain, Sebastien Jean, Kai Jia, Mikhail Korobov, Vivek Kulkarni, Alex Lamb, Pascal Lamblin, Eric Larsen, Cesar Laurent, Sean Lee, Simon Lefrancois, Simon Lemieux, Nicholas Leonard, Zhouhan Lin, Jesse A. Livezey, Cory Lorenz, Jeremiah Lowin, Qianli Ma, Pierre-Antoine Manzagol, Olivier Mastropietro, Robert T. McGibbon, Roland Memisevic, Bart van Merrienboer, Vincent Michalski, Mehdi Mirza, Alberto Orlandi, Christopher Pal, Razvan Pascanu, Mohammad Pezeshki, Colin Raffel, Daniel Renshaw, Matthew Rocklin, Adriana Romero, Markus Roth, Peter Sadowski, John Salvatier, Francois Savard, Jan Schluter, John Schulman, Gabriel Schwartz, Iulian Vlad Serban, Dmitriy Serdyuk, Samira Shabanian, Etienne Simon, Sigurd Spieckermann, S. Ramana Subramanyam, Jakub Sygnowski, Jeremie Tanguay, Gijs van Tulder, Joseph Turian, Sebastian Urban, Pascal Vincent, Francesco Visin, Harm de Vries, David Warde-Farley, Dustin J. Webb, Matthew Willson, Kelvin Xu, Lijun Xue, Li Yao, Saizheng Zhang, Ying Zhang
The Theano Development Team
arXiv:1605.02688 [cs.SC], (9 May 2016)
@article{al-rfou2016theano,

   title={Theano: A Python framework for fast computation of mathematical expressions},

   author={Al-Rfou, Rami and Alain, Guillaume and Almahairi, Amjad and Angermueller, Christof and Bahdanau, Dzmitry and Ballas, Nicolas and Bastien, Frederic and Bayer, Justin and Belikov, Anatoly and Belopolsky, Alexander and Bengio, Yoshua and Bergeron, Arnaud and Bergstra, James and Bisson, Valentin and Snyder, Josh Bleecher and Bouchard, Nicolas and Boulanger-Lewandowski, Nicolas and Bouthillier, Xavier and Brebisson, Alexandre de and Breuleux, Olivier and Carrier, Pierre-Luc and Cho, Kyunghyun and Chorowski, Jan and Christiano, Paul and Cooijmans, Tim and Cote, Marc-Alexandre and Cote, Myriam and Courville, Aaron and Dauphin, Yann N. and Delalleau, Olivier and Demouth, Julien and Desjardins, Guillaume and Dieleman, Sander and Dinh, Laurent and Ducoffe, Melanie and Dumoulin, Vincent and Kahou, Samira Ebrahimi and Erhan, Dumitru and Fan, Ziye and Firat, Orhan and Germain, Mathieu and Glorot, Xavier and Goodfellow, Ian and Graham, Matt and Gulcehre, Caglar and Hamel, Philippe and Harlouchet, Iban and Heng, Jean-Philippe and Hidasi, Balazs and Honari, Sina and Jain, Arjun and Jean, Sebastien and Jia, Kai and Korobov, Mikhail and Kulkarni, Vivek and Lamb, Alex and Lamblin, Pascal and Larsen, Eric and Laurent, Cesar and Lee, Sean and Lefrancois, Simon and Lemieux, Simon and Leonard, Nicholas and Lin, Zhouhan and Livezey, Jesse A. and Lorenz, Cory and Lowin, Jeremiah and Ma, Qianli and Manzagol, Pierre-Antoine and Mastropietro, Olivier and McGibbon, Robert T. and Memisevic, Roland and Merrienboer, Bart van and Michalski, Vincent and Mirza, Mehdi and Orlandi, Alberto and Pal, Christopher and Pascanu, Razvan and Pezeshki, Mohammad and Raffel, Colin and Renshaw, Daniel and Rocklin, Matthew and Romero, Adriana and Roth, Markus and Sadowski, Peter and Salvatier, John and Savard, Francois and Schluter, Jan and Schulman, John and Schwartz, Gabriel and Serban, Iulian Vlad and Serdyuk, Dmitriy and Shabanian, Samira and Simon, Etienne and Spieckermann, Sigurd and Subramanyam, S. Ramana and Sygnowski, Jakub and Tanguay, Jeremie and Tulder, Gijs van and Turian, Joseph and Urban, Sebastian and Vincent, Pascal and Visin, Francesco and Vries, Harm de and Warde-Farley, David and Webb, Dustin J. and Willson, Matthew and Xu, Kelvin and Xue, Lijun and Yao, Li and Zhang, Saizheng and Zhang, Ying},

   year={2016},

   month={may},

   archivePrefix={"arXiv"},

   primaryClass={cs.SC}

}

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Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers – especially in the machine learning community – and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models.

The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.

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