Deep Learning with Nonsmooth Objectives

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.