The Gauss–Newton Matrix

Here is the loss surface of a nonlinear model, with two parameters theta zero and theta one on the floor, and a point theta on the slope above a curved valley.

The true Hessian splits in two: J transpose J, called the Gauss-Newton matrix, plus a second term that multiplies each residual by the second derivative of the model.

The rest of the narration is in the book's Companion.