Definition
Plain language
A table showing how each output of a function responds to small changes in each input.
As stated in the literature
The matrix of first-order partial derivatives of a vector-valued function, characterizing local linear behavior.
Why it matters: Jacobians underpin backpropagation, sensitivity analysis, and stability arguments throughout machine learning.
For example, for a function mapping (x, y) to (x²+y, xy), the Jacobian's top row records how the first output changes with x and y respectively.
Heard on the show
“Specifically, you need to invert "the identity minus the Jacobian of the refinement step.”Episode 041 — When the Iteration Teaches the Model to Skip the Iteration