Papers › Forward-Mode Automatic Differentiation in Julia

Forward-Mode Automatic Differentiation in Julia

26 Jul 2016arXiv:1607.07892links table onlyarchive 2025-07-28

Jarrett Revels, Miles Lubin, Theodore Papamarkou

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We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as Python and MATLAB, ForwardDiff takes advantage of just-in-time (JIT) compilation to transparently recompile AD-unaware user code, enabling efficient support for higher-order differentiation and differentiation using custom number types (including complex numbers). For gradient and Jacobian calculations, ForwardDiff provides a variant of vector-forward mode that avoids expensive heap allocation and makes better use of memory bandwidth than traditional vector mode. In our numerical experiments, we demonstrate that for nontrivially large dimensions, ForwardDiff's gradient computations can be faster than a reverse-mode implementation from the Python-based autograd package. We also illustrate how ForwardDiff is used effectively within JuMP, a modeling language for optimization. According to our usage statistics, 41 unique repositories on GitHub depend on ForwardDiff, with users from diverse fields such as astronomy, optimization, finite element analysis, and statistics. This document is an extended abstract that has been accepted for presentation at the AD2016 7th International Conference on Algorithmic Differentiation.

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JuliaDiff/ForwardDiff.jl officialmentioned in papermentioned on GitHub report
Bmillidgework/AutoDiff.jl mentioned on GitHubNOASSERTION report
Klaus271/Knum mentioned on GitHubMIT report
chenyangzhu/Knum mentioned on GitHubMIT report
jesse-sharp/sharp2021b mentioned on GitHub report
mitmath/matrixcalc mentioned on GitHubjax report
storopoli/Bayesian-Julia mentioned on GitHubCC-BY-SA-4.0 report

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