  The efficacy of interpolating via Variably Scaled Kernels (VSKs) is known to
be dependent on the definition of a proper scaling function, but no numerical
recipes to construct it are available. Previous works suggest that such a
function should mimic the target one, but no theoretical evidence is provided.
This paper fills both the gaps: it proves that a scaling function reflecting
the target one may lead to enhanced approximation accuracy, and it provides a
user-independent tool for learning the scaling function by means of
Discontinuous Neural Networks ({\delta}NN), i.e., NNs able to deal with
possible discontinuities. Numerical evidence supports our claims, as it shows
that the key features of the target function can be clearly recovered in the
learned scaling function.
