Optimal scaling function selection critically affects VSK approximation quality. We derive error bounds involving Lebesgue functions, proving that scaling functions mimicking the target reduce pointwise error. This theoretical insight motivates learning the scaling function via discontinuous neural networks (δNNs). The δNN-VSK method jointly optimizes the scaling function and interpolation coefficients by minimizing interpolation error, while the VSK-f approach directly approximates the target. Numerical experiments confirm learned scaling functions closely resemble targets in both continuous and discontinuous cases. We also extend the VSK framework to multidimensional scaling functions for feature augmentation in kernel regularization networks and SVM classification.