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.

研究了 embedding geometry 对 softmax losses 在分类和图像检索任务中的影响，并提出了一个基于 von Mises-Fisher 分布的概率分类器，在产生改进的 out-of-the-box 校准的同时，与现有技术方法相比具有竞争力。

von Mises-Fisher 损失：探索嵌入式几何模型用于监督式学习

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

We are concerned with learning models that generalize well to different
\emph{unseen} domains. We consider a worst-case formulation over data
distributions that are near the source domain in the feature space. Only using
training data from a single source distribution, we propose an iterative
procedure that augments the dataset with examples from a fictitious target
domain that is "hard" under the current model. We show that our iterative
scheme is an adaptive data augmentation method where we append adversarial
examples at each iteration. For softmax losses, we show that our method is a
data-dependent regularization scheme that behaves differently from classical
regularizers that regularize towards zero (e.g., ridge or lasso). On digit
recognition and semantic segmentation tasks, our method learns models improve
performance across a range of a priori unknown target domains.

该篇研究论文提出了一个基于循环迭代的数据增强方法，使用虚构的目标领域中存在 “困难” 样本的数据来训练学习模型，以在先前未知的目标领域上实现更好的一般化表现。该方法利用对抗性示例以及数据依赖正则化来提高模型性能。