A review of automatic differentiation and its efficient implementation

By Charles C. Margossian. WIREs Data Mining Knowl. Discov., 2018

407 citations recorded by the source corpus.

Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation (AD) is a powerful tool to automate the calculation of derivatives and is preferable to more traditional methods, especially when differentiating complex algorithms and mathematical functions. The implementation of AD, however, requires some care to insure efficiency. Modern differentiation packages deploy a broad range of computational techniques to improve applicability, run time, and memory management. Among these techniques are operation overloading, region‐based memory, and expression templates. There also exist several mathematical techniques which can yield high performance gains when applied to complex algorithms. For example, semi‐analytical derivatives can reduce by orders of magnitude the runtime required to numerically solve and differentiate an algebraic equation. Open and practical problems include the extension of current packages to provide more specialized routines, and finding optimal methods to perform higher‐order differentiation.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/07bcc076a6cd0832eb9e83fa42c16efe5f2c2c89

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In Control and Systems Engineering

1. Xuhui Meng
2. Zhiping Mao
3. G. Em Karniadakis
4. Luke Metz
5. Lu Lu
6. Tal Kachman
7. Sam Schoenholz
8. C. Freeman

Citations in the corpus

• Gradients are Not All You Need (2021, background): “Automatic differentiation provides a conceptually straightforward handle for computing derivatives though these systems, and often can be applied with limited compute and memory overhead [Paszke et al., 2017, Ablin et al., 2020, Margossian, 2019, Bischof et al., 1991, Corliss et al., 2013].”
• DeepXDE: A Deep Learning Library for Solving Differential Equations (2019, methodology): “There are four possible methods for computing the derivatives [5, 38]: (1) hand-coded analytical derivative; (2) finite difference or other numerical approximations; (3) symbolic differentiation (used in software programs such as Mathematica, Maxima, and Maple); and (4) automatic differentiation (AD”