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:
“A chain is no stronger than its weakest link, and life is after all a chain.”
—William James (1842–1910)
“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 ...”)
“In societies where modern conditions of production prevail, all of life presents itself as an immense accumulation of spectacles. Everything that was directly lived has moved away into a representation.”
—Guy Debord (b. 1931)