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Differentiation lies at the core of many machine-learning algorithms, and is well-supported by popular autodiff systems, such as TensorFlow and PyTorch.
Some Cantor sets and Cantor functions
R. B. Darst · 1972
Earlier work this paper cites.
Principles of mathematical analysis
W. Rudin · 1976
Earlier work this paper cites.
Learning representations by back-propagating errors
D. E. Rumelhart, G. E. Hinton, and R. J. Williams · 1986
Earlier work this paper cites.
Optimization and nonsmooth analysis
F. H. Clarke · 1990
Earlier work this paper cites.
Geometric categories and o-minimal structures
L. van den Dries and C. Miller · 1996
Earlier work this paper cites.
Laws of chaos: Invariant measures and dynamical systems in one dimension
A. Boyarsky and P. Gora · 1997
Earlier work this paper cites.
Real analysis
A. M. Bruckner, J. B. Bruckner, and B. S. Thomson · 1997
Earlier work this paper cites.
Nonsmooth analysis and control theory
F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and P. R. Wolenski · 1998
Earlier work this paper cites.
Variational analysis
R. T. Rockafellar and R. J.-B. Wets · 1998
Earlier work this paper cites.
A primer of real analytic functions
S. G. Krantz and H. R. Parks · 2002
Earlier work this paper cites.
Counterexamples in analysis
B. R. Gelbaum and J. M. H. Olmsted · 2003
Earlier work this paper cites.
A mathematical model for automatic differentiation in machine learning
J. Bolte and E. Pauwels · 2006
Earlier work this paper cites.
Evaluating derivatives: Principles and techniques of algorithmic differentiation
A. Griewank and A. Walther · 2008
Earlier work this paper cites.
Reverse-mode AD in a functional framework: Lambda the ultimate backpropagator
B. A. Pearlmutter and J. M. Siskind · 2008
Earlier work this paper cites.
Theano: A CPU and GPU math compiler in Python
J. Bergstra, O. Breuleux, F. Bastien, P. Lamblin, R. Pascanu, G. Desjardins, J. Turian, D. Warde-Farley, and Y. Bengio · 2010
Earlier work this paper cites.
An introduction to measure theory
T. Tao · 2011
Cited alongside, same era.
Getting started with ADOL-C
A. Walther and A. Griewank · 2012
Cited alongside, same era.
The Tapenade automatic differentiation tool: Principles, model, and specification
L. Hascoët and V. Pascual · 2013
Cited alongside, same era.
Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
Cited alongside, same era.
Autograd: Effortless gradients in Numpy
D. Maclaurin, D. Duvenaud, and R. P. Adams · 2015
Cited alongside, same era.
The zero set of a real analytic function
B. Mityagin · 2015
Cited alongside, same era.
JAX: Composable transformations of Python+NumPy programs, 2018
J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, and S. Wanderman-Milne · 2018
Later among the works it cites.
Compiling machine learning programs via high-level tracing
R. Frostig, M. Johnson, and C. Leary · 2018
Later among the works it cites.
Provably correct automatic sub-differentiation for qualified programs
S. M. Kakade and J. D. Lee · 2018
Later among the works it cites.
Analysis of nonsmooth stochastic approximation: The differential inclusion approach
S. Majewski, B. Miasojedow, and E. Moulines · 2018
Later among the works it cites.
Tangent: Automatic differentiation using source-code transformation for dynamically typed array programming
B. van Merrienboer, D. Moldovan, and A. B. Wiltschko · 2018
Later among the works it cites.
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J. Schmidhuber · 2015
Cited alongside, same era.
TensorFlow: A system for large-scale machine learning
M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. A. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng · 2016
Cited alongside, same era.
Diffsharp: An AD library for .NET languages
A. G. Baydin, B. A. Pearlmutter, and J. M. Siskind · 2016
Cited alongside, same era.
Deep learning
I. Goodfellow, Y. Bengio, and A. Courville · 2016
Cited alongside, same era.
On Lipschitz optimization based on gray-box piecewise linearization
A. Griewank, A. Walther, S. Fiege, and T. Bosse · 2016
Cited alongside, same era.
Modeling, inference and optimization with composable differentiable procedures
D. Maclaurin · 2016
Cited alongside, same era.
G. A. Edgar · 2019
Later among the works it cites.
A review of automatic differentiation and its efficient implementation
C. C. Margossian · 2019
Later among the works it cites.
PyTorch: An imperative style, high-performance deep learning library
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köpf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala · 2019
Later among the works it cites.
Chainer: A deep learning framework for accelerating the research cycle
S. Tokui, R. Okuta, T. Akiba, Y. Niitani, T. Ogawa, S. Saito, S. Suzuki, K. Uenishi, B. Vogel, and H. Y. Vincent · 2019
Later among the works it cites.
Demystifying differentiable programming: Shift/reset the penultimate backpropagator
F. Wang, D. Zheng, J. M. Decker, X. Wu, G. M. Essertel, and T. Rompf · 2019
Later among the works it cites.
LF-PPL: A low-level first order probabilistic programming language for non-differentiable models
Y. Zhou, B. J. Gram-Hansen, T. Kohn, T. Rainforth, H. Yang, and F. Wood · 2019
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A simple differentiable programming language
M. Abadi and G. D. Plotkin · 2020
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Stochastic subgradient method converges on tame functions
D. Davis, D. Drusvyatskiy, S. M. Kakade, and J. D. Lee · 2020
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Correctness of automatic differentiation via diffeologies and categorical gluing
M. Huot, S. Staton, and M. Vákár · 2020
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Densities of almost-surely terminating probabilistic programs are differentiable almost everywhere
C. Mak, C. L. Ong, H. Paquet, and D. Wagner · 2020
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