Circle Loss: A Unified Perspective of Pair Similarity Optimization

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.

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Results from the Paper

 Ranked #1 on Face Verification on IJB-C (training dataset metric)

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Metric Learning CARS196 CircleLoss R@1 83.4 # 23
Face Recognition CFP-FP CircleLoss(ours) Accuracy 0.9602 # 5
Face Verification IJB-C circle loss TAR @ FAR=1e-3 96.29% # 5
TAR @ FAR=1e-4 93.95% # 17
TAR @ FAR=1e-5 89.60% # 10
training dataset MS1M Cleaned # 1
model R100 # 1
Face Recognition LFW CircleLoss Accuracy 0.9973 # 5
Person Re-Identification Market-1501 MGN + CircleLoss(ours) Rank-1 96.1 # 16
mAP 87.4 # 50
Person Re-Identification Market-1501 ResNet50 + CircleLoss(ours) Rank-1 94.2 # 54
mAP 84.9 # 59
Person Re-Identification MSMT17 MGN + CircleLoss(ours) Rank-1 76.9 # 21
mAP 52.1 # 20
Person Re-Identification MSMT17 ResNet50 + CircleLoss(ours) Rank-1 76.3 # 22
mAP 50.2 # 21
Metric Learning Stanford Online Products Circle Loss R@1 78.3 # 18