  Humans can count very fast by subitizing, but slow substantially as the
number of objects increases. Previous studies have shown a trained deep neural
network (DNN) detector can count the number of objects in an amount of time
that increases slowly with the number of objects. Such a phenomenon suggests
the subitizing ability of DNNs, and unlike humans, it works equally well for
large numbers. Many existing studies have successfully applied DNNs to object
counting, but few studies have studied the subitizing ability of DNNs and its
interpretation. In this paper, we found DNNs do not have the ability to
generally count connected components. We provided experiments to support our
conclusions and explanations to understand the results and phenomena of these
experiments. We proposed three ML-learnable characteristics to verify learnable
problems for ML models, such as DNNs, and explain why DNNs work for specific
counting problems but cannot generally count connected components.
