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Register a new userA Review of automatic differentiation and its efficient implementation
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Authors
Charles C. Margossian
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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 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 automatic differentiation 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 problems include the extension of current packages to provide more specialized routines, and efficient methods to perform higher-order differentiation.
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Automatic differentiation is a set of techniques to efficiently and accurately compute the derivative of a function represented by a computer program. Existing C++ libraries for automatic differentiation (e.g. Adept, Stan Math Library), however, exhibit large memory consumptions and runtime performance issues. This paper introduces FastAD, a new C++ template library for automatic differentiation, that overcomes all of these challenges in existing libraries by using vectorization, simpler memory management using a fully expression-template-based design, and other compile-time optimizations to remove some run-time overhead. Benchmarks show that FastAD performs 2-10 times faster than Adept and 2-19 times faster than Stan across various test cases including a few real-world examples.
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