Chain Rules for Hessian and Higher Derivatives Made Easy by Tensor Calculus

Formulae for high derivatives of composite functions

LE Fraenkel · 1978

Earlier work this paper cites.

Acegen, acefem, 2007

Jože Korelc · 2007

Earlier work this paper cites.

Differential calculus, tensor products and the importance of notation

Original

Jonathan H Manton · 2012

Earlier work this paper cites.

TensorFlow: Large-scale machine learning on heterogeneous systems, 2015

Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dan Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng · 2015

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The equality of mixed partial derivatives under weak differentiability conditions

Ettore Minguzzi · 2015

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Sympy: symbolic computing in python

Aaron Meurer, Christopher P. Smith, Mateusz Paprocki, Ondřej Čertík, Sergey B. Kirpichev, Matthew Rocklin, AMiT Kumar, Sergiu Ivanov, Jason K. Moore, Sartaj Singh, Thilina Rathnayake, Sean Vig, Brian E. Granger, Richard P. Muller, Francesco Bonazzi, Harsh Gupta, Shivam Vats, Fredrik Johansson, Fabian Pedregosa, Matthew J. Curry, Andy R. Terrel, Štěpán Roučka, Ashutosh Saboo, Isuru Fernando, Sumith Kulal, Robert Cimrman, and Anthony Scopatz · 2017

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Computing higher order derivatives of matrix and tensor expressions

Sören Laue, Matthias Mitterreiter, and Joachim Giesen · 2018

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