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Supervision for metric learning has long been given in the form ofequivalence between human-labeled classes. Although this type of supervisionhas been a basis of metric learning for decades, we argue that it hindersfurther advances in the field. In this regard, we propose a new regularizationmethod, dubbed HIER, to discover the latent semantic hierarchy of trainingdata, and to deploy the hierarchy to provide richer and more fine-grainedsupervision than inter-class separability induced by common metric learninglosses.HIER achieves this goal with no annotation for the semantic hierarchybut by learning hierarchical proxies in hyperbolic spaces. The hierarchicalproxies are learnable parameters, and each of them is trained to serve as anancestor of a group of data or other proxies to approximate the semantichierarchy among them. HIER deals with the proxies along with data in hyperbolicspace since the geometric properties of the space are well-suited to representtheir hierarchical structure. The efficacy of HIER is evaluated on fourstandard benchmarks, where it consistently improved the performance ofconventional methods when integrated with them, and consequently achieved thebest records, surpassing even the existing hyperbolic metric learningtechnique, in almost all settings.

HIER: Metric Learning Beyond Class Labels via Hierarchical Regularization