Compute the Jacobian matrix of func with respect to each input.

The Jacobian of a vector-valued function $f : \mathbb{R}^n \to \mathbb{R}^m$ is

Lucid evaluates it row-by-row by repeated reverse-mode backward passes — one per output element — seeding each pass with a one-hot cotangent so the resulting input gradient is exactly the corresponding Jacobian row. The cost therefore scales with the output dimension $m$; prefer vjp when only $v^\top J$ is needed and jvp when only $J v$ is needed.