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:
“Man ... cannot learn to forget, but hangs on the past: however far or fast he runs, that chain runs with him.”
—Friedrich Nietzsche (1844–1900)
“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)
““Under an accumulation of staggerers, no man can be considered a free agent. No man knocks himself down; if his destiny knocks him down, his destiny must pick him up again.””
—Charles Dickens (1812–1870)