  We show that the learning sample complexity of a sigmoidal neural network
constructed by Sontag (1992) required to achieve a given misclassification
error under a fixed purely atomic distribution can grow arbitrarily fast: for
any prescribed rate of growth there is an input distribution having this rate
as the sample complexity, and the bound is asymptotically tight. The rate can
be superexponential, a non-recursive function, etc. We further observe that
Sontag's ANN is not Glivenko-Cantelli under any input distribution having a
non-atomic part.
