Analytic (or automatic) derivatives of a KRR model?

[dpadula85]

Hello,

I have a KRR model, and I checked that it is differentiable computing numeric derivatives.
Although the calculation is fast, I would like to know whether there is a way to get analytic or automatic derivatives of the function with respect to input features, besides me doing the math for said derivatives.

To give more information, each input feature is an inverse euclidean distance $\frac{1}{r_{ij}} = \frac{1}{\lvert r_i - r_j \rvert}$ between two points, so I would actually need the derivative with respect to cartesian displacements $\left( \frac{\partial f}{\partial x_i}, \frac{\partial f}{\partial y_i}, \frac{\partial f}{\partial z_i} \right)$.