Abstract

Automatic Differentiation (aka Algorithmic Differentiation, aka Computational Differentiation, aka AD) is an established discipline concerning methods of transforming algorithmic processes (ie, computer programs) which calculate numeric functions to also calculate various derivatives of interest, and ways of using such methods. We begin with a discussion of the venerable history of the field, whose roots go back to the dawn of the computer age. There are various “modes” of automatic differentiation, and we will describe forward, reverse, and checkpoint-reverse modes in detail. We then turn our attention to existing systems, with a focus on those able to attain high performance, and the implementation techniques which allow this. These implementations have a variety of weaknesses and restrictions which, we will argue, have impeded the uptake of AD. We close with a benchmark comparing the fastest current systems with our own research prototype compiler based on principles discussed in Part Two. (Joint work with Jeffrey Mark Siskind.)