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Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age.
Use of automatic differentiation for calculating Hessians and Newton steps
L. C. Dixon · 1991
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Fast exact multiplication by the hessian
B. A. Pearlmutter · 1994
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Regularization tools for training large feed-forward neural networks using automatic differentiation
J. Eriksson, M. Gulliksson, P. Lindström, and P. Wedin · 1998
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Gradient-based optimization of hyper-parameters
Y. Bengio · 2000
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Choosing multiple parameters for support vector machines
O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee · 2002
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Accelerated training of conditional random fields with stochastic gradient methods
S. V. N. Vishwanathan, N. N. Schraudolph, M. W. Schmidt, and K. P. Murphy · 2006
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Algorithmic differentiation: Application to variational problems in computer vision
T. Pock, M. Pock, and H. Bischof · 2007
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Automatic differentiation of explicit Runge-Kutta methods for optimal control
A. Walther · 2007
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Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation
R. K. Al Seyab and Y. Cao · 2008
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On the implementation of automatic differentiation tools
C. H. Bischof, P. D. Hovland, and B. Norris · 2008
Cited alongside, same era.
Automatic differentiation for GPU-accelerated 2D/3D registration
M. Grabner, T. Pock, T. Gross, and B. Kainz · 2008
Cited alongside, same era.
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
A. Griewank and A. Walther · 2008
Cited alongside, same era.
Using programming language theory to make AD sound and efficient
B. A. Pearlmutter and J. M. Siskind · 2008
A memoryless BFGS neural network training algorithm
M. S. Apostolopoulou, D. G. Sotiropoulos, I. E. Livieris, and P. Pintelas · 2009
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Efficient computation of sparse Hessians using coloring and automatic differentiation
A. Gebremedhin, A. Pothen, A. Tarafdar, and A. Walther · 2009
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The Image Processing Handbook
J. C. Russ · 2010
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MCMC for using Hamiltonian dynamics
R. Neal · 2011
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Optimization for Machine Learning
S. Sra, S. Nowozin, and S. J. Wright · 2011
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A. Radul, B. A. Pearlmutter, and J. M. Siskind · 2012
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Cited alongside, same era.
Application of PID controller based on BP neural network using automatic differentiation method
W. Yang, Y. Zhao, L. Yan, and X. Chen · 2008
Cited alongside, same era.
Using polyvariant union-free flow analysis to compile a higher-order functional-programming language with a first-class derivative operator to efficient Fortran-like code
J. M. Siskind and B. A. Pearlmutter
Cited in the paper.
Nesting forward-mode AD in a functional framework
J. M. Siskind and B. A. Pearlmutter
Cited in the paper.