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.

翻译：摘要：长期以来，度量学习的监督信息以人工标注类别间的等价形式提供。尽管这种监督方式已成为度量学习数十年的基础，但我们认为这阻碍了该领域的进一步发展。为此，我们提出一种名为HIER的新型正则化方法，旨在发现训练数据中的潜在语义层次结构，并通过该层次结构提供比常见度量学习损失所导致的类间可分性更丰富、更细粒度的监督信息。HIER无需对语义层次进行标注，而是通过在双曲空间中学习层次代理来实现这一目标。这些层次代理是可学习参数，每个代理被训练为数据组或其他代理的祖先节点，以近似它们之间的语义层级关系。由于双曲空间的几何特性非常适合表示层次结构，HIER在双曲空间中同时处理代理与数据。我们在四个标准基准上评估了HIER的有效性，结果显示，当与常规方法结合时，它能够持续提升其性能，并在几乎所有设定下创下最佳记录，甚至超越了现有的双曲度量学习技术。