  Artificial neural nets can represent and classify many types of data but are
often tailored to particular applications -- e.g., for "fair" or "hierarchical"
classification. Once an architecture has been selected, it is often difficult
for humans to adjust models for a new task; for example, a hierarchical
classifier cannot be easily transformed into a fair classifier that shields a
protected field. Our contribution in this work is a new neural network
architecture, the concept subspace network (CSN), which generalizes existing
specialized classifiers to produce a unified model capable of learning a
spectrum of multi-concept relationships. We demonstrate that CSNs reproduce
state-of-the-art results in fair classification when enforcing concept
independence, may be transformed into hierarchical classifiers, or even
reconcile fairness and hierarchy within a single classifier. The CSN is
inspired by existing prototype-based classifiers that promote interpretability.
