Forward-Mode Automatic Differentiation in Julia

TL;DR

ForwardDiff is a Julia package that provides high-performance forward-mode automatic differentiation, enabling efficient higher-order derivatives and custom number types, often outperforming reverse-mode AD in large dimensions.

Contribution

It introduces a JIT-compiled forward-mode AD tool in Julia that supports higher-order derivatives and custom types with performance comparable to low-level languages.

Findings

ForwardDiff's gradient computation can be faster than reverse-mode in large dimensions.

It supports higher-order derivatives and custom number types efficiently.

Widely used across diverse scientific fields, with 41 GitHub repositories depending on it.

Abstract

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.