#jacobian

Question 1: Select all that apply

A program computes $f: \mathbb{R}^N \to \mathbb{R}^M$ , and you want its full $M \times N$ Jacobian by automatic differentiation. Which statements are correct? Select all that apply.

Forward and reverse mode give the same derivatives, up to floating-point rounding1
Forward mode needs one pass per input, so its cost grows with $N$ 2
Reverse mode needs one pass per output, so its cost grows with $M$ 3
Reverse mode always needs less time and less memory than forward mode4

Timed test