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Recent work has argued that classification losses utilizing softmaxcross-entropy are superior not only for fixed-set classification tasks, butalso by outperforming losses developed specifically for open-set tasksincluding few-shot learning and retrieval. Softmax classifiers have beenstudied using different embedding geometries -- Euclidean, hyperbolic, andspherical -- and claims have been made about the superiority of one or another,but they have not been systematically compared with careful controls. Weconduct an empirical investigation of embedding geometry on softmax losses fora variety of fixed-set classification and image retrieval tasks. An interestingproperty observed for the spherical losses lead us to propose a probabilisticclassifier based on the von Mises-Fisher distribution, and we show that it iscompetitive with state-of-the-art methods while producing improvedout-of-the-box calibration. We provide guidance regarding the trade-offsbetween losses and how to choose among them.

von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learning