Stability of neural networks for slightly perturbed training data sets

In learning models of artificial neural networks, that randomness comes from the distribution of the training data. We show individual observations do not affect excessively for a neutral network modeling, provided that it has adequate nodes on the hidden layer and proves that the empirical error of a neural network with p number of weights converges to the expected error when p/ m → 0 where m is the size of the perturbed training data.