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 the chain, chain, reverse and/or accumulation:
“I was
the girl of the chain letter,
the girl full of talk of coffins and keyholes,
the one of the telephone bills,
the wrinkled photo and the lost connections....”
—Anne Sexton (1928–1974)
“The name of the town isn’t important. It’s the one that’s just twenty-eight minutes from the big city. Twenty-three if you catch the morning express. It’s on a river and it’s got houses and stores and churches. And a main street. Nothing fancy like Broadway or Market, just plain Broadway. Drug, dry good, shoes. Those horrible little chain stores that breed like rabbits.”
—Joseph L. Mankiewicz (1909–1993)
“Now listen, buddy, there are a few corny ideas you got to get out of your head if you’re going to fly an airplane. Most things are just the reverse from what people think. The higher you are the safer you are. The Earth down there, that, that’s your enemy because once you hit that, boy, you splatter.”
—Dalton Trumbo (1905–1976)
“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)