Before revision:  We identify two methods in which the curse of dimensionality can be broken.The first approach constructs subsets of C(\mathcal{X ,\mathcal{P}_1( \mathcal{Y can be efficiently approximated .
After revision:  We identify two methods in which the curse of dimensionality "; i.e.: the number of parameters determining the approximating neural network depends only polynomially on the involved dimension and the approximation error. The first solution describes functions in C(\mathbb{R ,\mathcal{P}_1( \mathcal{Y can be efficiently approximated .