We study how certain smoothness constraints, for example, piecewise continuity, can be generalized from a discrete set of analog-valued data, by modifying the error backpropagation, learning algorithm. Numerical simulations demonstrate that by imposing two heuristic objectives — (1) reducing the number of hidden units, and (2) minimizing the magnitudes of the weights in the network — during the learning process, one obtains a network with a response function that smoothly interpolates between the training data.