Before revision:  We show the following paradox . There are basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities, however, there does not exist any algorithm, even randomised, that can train (or compute) such a NN. Indeed, for any positive integers K > 2 and L, there are cases where simultaneously:
After revision:  We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities, however, there does not exist any algorithm, even randomised, that can train (or compute) such a NN. Indeed, for any positive integers K > 2 and L, there are cases where simultaneously: