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Person Re-IDentification (ReID) aims at re-identifying persons from different viewpoints across multiple cameras. Capturing the fine-grained appearance differences is often the key to accurate person ReID, because many identities can be differentiated only when looking into these fine-grained differences. However, most state-of-the-art person ReID approaches, typically driven by a triplet loss, fail to effectively learn the fine-grained features as they are focused more on differentiating large appearance differences. To address this issue, we introduce a novel pairwise loss function that enables ReID models to learn the fine-grained features by adaptively enforcing an exponential penalization on the images of small differences and a bounded penalization on the images of large differences. The proposed loss is generic and can be used as a plugin to replace the triplet loss to significantly enhance different types of state-of-the-art approaches. Experimental results on four benchmark datasets show that the proposed loss substantially outperforms a number of popular loss functions by large margins; and it also enables significantly improved data efficiency.