We address the problem of distance metric learning (DML), defined as learning
a distance consistent with a notion of semantic similarity. Traditionally, for
this problem supervision is expressed in the form of sets of points that follow
an ordinal relationship -- an anchor point $x$ is similar to a set of positive
points $Y$, and dissimilar to a set of negative points $Z$, and a loss defined
over these distances is minimized. While the specifics of the optimization
differ, in this work we collectively call this type of supervision Triplets and
all methods that follow this pattern Triplet-Based methods. These methods are
challenging to optimize. A main issue is the need for finding informative
triplets, which is usually achieved by a variety of tricks such as increasing
the batch size, hard or semi-hard triplet mining, etc. Even with these tricks,
the convergence rate of such methods is slow. In this paper we propose to
optimize the triplet loss on a different space of triplets, consisting of an
anchor data point and similar and dissimilar proxy points which are learned as
well. These proxies approximate the original data points, so that a triplet
loss over the proxies is a tight upper bound of the original loss. This
proxy-based loss is empirically better behaved. As a result, the proxy-loss
improves on state-of-art results for three standard zero-shot learning
datasets, by up to 15% points, while converging three times as fast as other
triplet-based losses.

使用 proxy 点的三元组损失函数能够更快速地优化距离度量学习，提高零样本学习数据集的精度至多 15％，且比其他三元组损失函数的收敛速度块 3 倍。