# Circle Loss: A Unified Perspective of Pair Similarity Optimization

arXiv: https://arxiv.org/abs/2002.10857 · HTML: https://mlsanity.com/paper/2002.10857/

## Key facts

- Cited by 403 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2020.

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## Abstract (arXiv)

This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity sp and minimize the between-class similarity sn. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed sn and sp into similarity pairs and seek to reduce (sn-sp). 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 (sn-sp). 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.