This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity $s_p$ and minimize the between-class similarity $s_n$. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed $s_n$ and $s_p$ into similarity pairs and seek to reduce $(s_n-s_p)$. Such an optimization manner is inflexible, because the penalty strength on every single similarity score is restricted to be equal. Our intuition is that if a similarity score deviates far from the optimum, it should be emphasized. To this end, we simply re-weight each similarity to highlight the less-optimized similarity scores. It results in a Circle loss, which is named due to its circular decision boundary. The Circle loss has a unified formula for two elemental deep feature learning approaches, i.e. learning with class-level labels and pair-wise labels. Analytically, we show that the Circle loss offers a more flexible optimization approach towards a more definite convergence target, compared with the loss functions optimizing $(s_n-s_p)$. Experimentally, we demonstrate the superiority of the Circle loss on a variety of deep feature learning tasks. On face recognition, person re-identification, as well as several fine-grained image retrieval datasets, the achieved performance is on par with the state of the art.

本文提供了一个对深度特征学习进行相似性优化的观点，介绍了一种更灵活的Circle损失函数，并且在人脸识别、人员重新识别以及一些细粒度图像检索数据集上展示了Circle损失的卓越性能。

Circle Loss：一种统一的对偶相似性优化视角