SO-softmax loss for discriminable embedding learning in CNNs

Abstract

Convolutional neural networks (CNNs)-based classifiers, trained with the softmax cross-entropy loss, have achieved remarkable success in learning embeddings for pattern recognition. The cosine similarity-based softmax variants further improve the performance by focusing on optimizing the angles between embeddings and class weights. However, embeddings learned by these variants still have significant intra-class variances since these methods only optimize the relative differences between intra- and inter-class cosine similarities. To simultaneously optimize intra- and inter-class cosine similarities, this paper proposes a cosine Similarity Optimization-based softmax (SO-softmax) loss, which is based on a generalized softmax loss formulation that combines both similarities. The proposed loss constrains the intra-class (positive) and inter-class (negative) cosine similarity by quadratic transformations, thus making the embedding representation more compact within classes and more distinguishable between classes. It is verified theoretically that SO-softmax loss can optimize both the similarities simultaneously. Thorough experiments are conducted on typical audio classification, image classification, face verification, image retrieval, and person re-identification tasks, and the results show that SO-softmax loss outperforms the state-of-the-art loss functions in CNNs-based frameworks.