Recent work has argued that classification losses utilizing softmax cross-entropy are superior not only for fixed-set classification tasks, but also by outperforming losses developed specifically for open-set tasks including few-shot learning and retrieval. Softmax classifiers have been studied using different embedding geometries -- Euclidean, hyperbolic, and spherical -- and claims have been made about the superiority of one or another, but they have not been systematically compared with careful controls. We conduct an empirical investigation of embedding geometry on softmax losses for a variety of fixed-set classification and image retrieval tasks. An interesting property observed for the spherical losses lead us to propose a probabilistic classifier based on the von Mises--Fisher distribution, and we show that it is competitive with state-of-the-art methods while producing improved out-of-the-box calibration. We provide guidance regarding the trade-offs between losses and how to choose among them.

翻译：最近的工作认为,利用软麦角交叉作物的分类损失,不仅对固定定级任务而言,而且对专门为开放任务(包括短短的学习和检索)而开发的超效损失,都具有优越性。软麦分级器使用不同的嵌入式地貌(Euclidean, 双曲, 球体)进行了研究,对其中一方或另一方的优越性提出了索赔,但并没有系统地与谨慎的控制措施进行比较。我们进行了实验性调查,对将软麦分层的几何测量嵌入软麦分层,以适应各种固定定级和图像检索任务。观测到的球体损失的一个有趣的属性导致我们提出一个基于冯米斯-费舍分布的概率性分类器,我们表明,在产生改进的箱外校准时,它与最新的方法具有竞争力。我们为损失的权衡和如何选择提供了指导。