The Chain Rule, Forward and Reverse Accumulation
Fundamental to AD is the decomposition of differentials provided by the chain rule. For the simple composition the chain rule gives
Usually, two distinct modes of AD are presented, forward accumulation (or forward mode) and reverse accumulation (or reverse mode). Forward accumulation specifies that one traverses the chain rule from right to left (that is, first one computes and then ), while reverse accumulation has the traversal from left to right.
Read more about this topic: Automatic Differentiation
Famous quotes containing the words chain, reverse and/or accumulation:
“Oft, in the stilly night, Ere Slumber’s chain has bound me, Fond Memory brings the light Of other days around me.”
—Thomas Moore (1779–1852)
“They shall beat their swords into plowshares, and their spears into pruninghooks: nation shall not lift up sword against nation, neither shall they learn war any more.”
—Bible: Hebrew Isaiah, 2:4.
The words reappear in Micah 4:3, and the reverse injunction is made in Joel 3:10 (”Beat your plowshares into swords ...”)
“You watched and you saw what happened and in the accumulation of episodes you saw the pattern: Daddy ruled the roost, called the shots, made the money, made the decisions, so you signed up on his side, and fifteen years later when the women’s movement came along with its incendiary manifestos telling you to avoid marriage and motherhood, it was as if somebody put a match to a pile of dry kindling.”
—Anne Taylor Fleming (20th century)