Learning deep discriminative embeddings via joint rescaled features and log-probability centers

•Extend center loss to log probability space for better generalization.•Modify center loss for better geometry interpretation.•Rescale deep features for better discrimination.•Theory analysis is provided for ground support. Recently softmax based loss functions have surged to advance image classification and face verification. Most efforts boost discrimination of the softmax loss by using novel angular margins in varying ways, but few analyze where the discrimination truly comes from whilst considering the power of relieving the overfitting to enhance the softmax loss. In this paper, we firstly delve into such mainstream of softmax based loss functions in theory, and recognize the importance of easing overfitting to the softmax loss. In terms of such analysis, this paper intends to bring the softmax loss up to the competitive level with current well-behaved loss functions. We do this in two ways: (1) regularizing the softmax to relieve the overfitting by learning the log-probability centers, and (2) rescaling deep embeddings of the softmax with a constant scale to further enhance inter-class separability in Euclidean space. We call the resulting loss function rLogCenter loss for short. Simple and interpretable as our loss is, it guides CNNs to induce performance gains in the experiments of both image classification and face verification.