Understanding Metric Learning on Unit Hypersphere and Generating Better Examples for Adversarial Training

Recent works have shown that adversarial examples can improve the performance of representation learning tasks. In this paper, we boost the performance of deep metric learning (DML) models with adversarial examples generated by attacking two new objective functions: \textit{intra-class alignment} and \textit{hyperspherical uniformity}. These two new objectives come from our theoretical and empirical analysis of the tuple-based metric losses on the hyperspherical embedding space. Our analytical results reveal that a) the metric losses on positive sample pairs are related to intra-class alignment; b) the metric losses on negative sample pairs serve as uniformity regularization on hypersphere. Based on our new understanding on the DML models, we propose Adversarial Deep Metric Learning model with adversarial samples generated by Alignment or Uniformity objective (ADML+A or U). With the same network structure and training settings, ADML+A and ADML+U consistently outperform the state-of-the-art vanilla DML models and a baseline model, adversarial DML model with attacking triplet objective function, on four metric learning benchmarks.