  Though deep learning has pushed the boundaries of classification forward, in
recent years hints of the limits of standard classification have begun to
emerge. Problems such as fooling, adding new classes over time, and the need to
retrain learning models only for small changes to the original problem all
point to a potential shortcoming in the classic classification regime, where a
comprehensive a priori knowledge of the possible classes or concepts is
critical. Without such knowledge, classifiers misjudge the limits of their
knowledge and overgeneralization therefore becomes a serious obstacle to
consistent performance. In response to these challenges, this paper extends the
classic regime by reframing classification instead with the assumption that
concepts present in the training set are only a sample of the hypothetical
final set of concepts. To bring learning models into this new paradigm, a novel
elaboration of standard architectures called the competitive overcomplete
output layer (COOL) neural network is introduced. Experiments demonstrate the
effectiveness of COOL by applying it to fooling, separable concept learning,
one-class neural networks, and standard classification benchmarks. The results
suggest that, unlike conventional classifiers, the amount of generalization in
COOL networks can be tuned to match the problem.
