Circle Loss: A Unified Perspective of Pair Similarity Optimization

2020/02/25 by Yifan Sun, Sun, Yifan, Changmao Cheng +11 · 29 citations
Computer Science · #Advanced Image and Video Retrieval Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Face recognition and analysis #Video Surveillance and Tracking Methods

paper · pdf · doi:10.48550/arxiv.2002.10857

openalex publication_date 2020/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Large-Margin Softmax Loss for Convolutional Neural Networks
• In Defense of the Triplet Loss for Person Re-Identification
• SphereFace: Deep Hypersphere Embedding for Face Recognition
• CosFace: Large Margin Cosine Loss for Deep Face Recognition
• Attention-based Ensemble for Deep Metric Learning
• Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning
• Deep Residual Learning for Image Recognition
• MS-Celeb-1M: A Dataset and Benchmark for Large-Scale Face Recognition
• L2-constrained Softmax Loss for Discriminative Face Verification

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