  Supervision for metric learning has long been given in the form of
equivalence between human-labeled classes. Although this type of supervision
has been a basis of metric learning for decades, we argue that it hinders
further advances in the field. In this regard, we propose a new regularization
method, dubbed HIER, to discover the latent semantic hierarchy of training
data, and to deploy the hierarchy to provide richer and more fine-grained
supervision than inter-class separability induced by common metric learning
losses.HIER achieves this goal with no annotation for the semantic hierarchy
but by learning hierarchical proxies in hyperbolic spaces. The hierarchical
proxies are learnable parameters, and each of them is trained to serve as an
ancestor of a group of data or other proxies to approximate the semantic
hierarchy among them. HIER deals with the proxies along with data in hyperbolic
space since the geometric properties of the space are well-suited to represent
their hierarchical structure. The efficacy of HIER is evaluated on four
standard benchmarks, where it consistently improved the performance of
conventional methods when integrated with them, and consequently achieved the
best records, surpassing even the existing hyperbolic metric learning
technique, in almost all settings.
