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Why do you say this is quite different from symbolic differentiation? It seems every function (including addition, multiplication, etc.) is simply augmented wit
by Chinjut 11y ago
Why do you say this is quite different from symbolic differentiation? It seems every function (including addition, multiplication, etc.) is simply augmented with a description of its total derivative, and these derivatives are combined via the chain rule, which is just how symbolic differentiation would normally be carried out as well.
- versteegen 11y agoYes, but in practice the difference is vast. You can apply automatic differentiation to (almost) arbitrary code with conditional branches, arbitrary inputs (by treating them as unknown constants wrt to the independent variables), recursion and for/while loops with an unknown number of loops, etc. Trying to describe all that using piecewise or recursive functions and then symbolically differentiate it is either a nightmare or impossible. Hence, automatic differentiation.