  We explore the potential for using a nonsmooth loss function based on the
max-norm in the training of an artificial neural network. We hypothesise that
this may lead to superior classification results in some special cases where
the training data is either very small or unbalanced.
  Our numerical experiments performed on a simple artificial neural network
with no hidden layers (a setting immediately amenable to standard nonsmooth
optimisation techniques) appear to confirm our hypothesis that uniform
approximation based approaches may be more suitable for the datasets with
reliable training data that either is limited size or biased in terms of
relative cluster sizes.
