# Circle Loss: A Unified Perspective of Pair Similarity Optimization

**Authors:** Yifan Sun, Changmao Cheng, Yuhan Zhang, Chi Zhang, Liang Zheng, Zhongdao Wang, Yichen Wei  
**arXiv:** [2002.10857](https://arxiv.org/abs/2002.10857)  
**Date:** 2020-02-25  
**Summary page:** https://www.summarizepaper.com/en/paper/2002.10857v1/

## Key points

- Introduces the Circle loss, a novel approach to optimize pair similarity in deep feature learning
- Goal is to maximize within-class similarity ($s_p$) and minimize between-class similarity ($s_n$)
- Existing loss functions embed $s_n$ and $s_p$ into similarity pairs and aim to reduce their difference $(s_n-s_p)$ but are inflexible due to equal penalty strength for all scores
- Authors propose re-weighting each score based on its deviation from the optimum, resulting in the Circle loss with a circular decision boundary
- Offers a unified formula for learning with class-level labels and pair-wise labels
- Provides more flexible optimization by emphasizing less-optimized scores as convergence targets
- Experimental results show outperformance of state-of-the-art methods on tasks like face recognition, person re-identification, and fine-grained image retrieval datasets
- Presents an innovative perspective on optimizing pair similarity in deep feature learning through the Circle loss, offering improved flexibility and convergence targets compared to existing methods

## Summary

This paper introduces the Circle loss, a novel approach to optimize pair similarity in deep feature learning. The goal is to maximize within-class similarity ($s_p$) and minimize between-class similarity ($s_n$). Existing loss functions embed $s_n$ and $s_p$ into similarity pairs and aim to reduce their difference $(s_n-s_p)$ but are inflexible due to equal penalty strength for all scores. To address this limitation, the authors propose re-weighting each score based on its deviation from the optimum, resulting in the Circle loss with a circular decision boundary. It offers a unified formula for two fundamental approaches: learning with class-level labels and pair-wise labels. Analytically, it provides a more flexible optimization by emphasizing less-optimized scores as convergence targets. Experimental results show that it outperforms state-of-the-art methods on various tasks like face recognition, person re-identification, and fine-grained image retrieval datasets. In conclusion, this paper presents an innovative perspective on optimizing pair similarity in deep feature learning through the Circle loss which offers improved flexibility and convergence targets compared to existing methods.