I understand conceptually how backpropagation works according to the chain rule, and I understand that partial derivatives calculate the rate of change of a function containing multiple variables with respect to one of those variables, the rest being fixed.
What I'm struggling with is what the value from these partial derivatives actually relates to. I found this https://activecalculus.org/multi/S-10-2-First-Order-Partial-Derivatives.html which gives some good examples. But with a NN I'm not sure what units the results of the derivatives relate to.
One of the examples on the website used z = f(x,y) z horizontal distance travelled of a projectile, x initial speed in feet per second, and y was the angle. So if taking the partial derivative with respect to x the results tell us how much the distance travelled changes with respect to the change in speed. So it might be that for every one foot per second increase of the initial speed, we get an increase of 8 feet horizontal travel if using a fixed value for y.
But when calculating the derivatives for backpropagation, does this mean that if we get an answer of (random value) 0.08, this means that for every change of 1 to the non-static variable we would get a change of 0.08 to our output? And what units (if any) do these values relate to?