Title: Determinant regularization for Deep Metric Learning. Abstract: Distance Metric Learning (DML) aims to learn the distance metric that better reflects the semantical similarities in the data. Current \textit{pair-based} and \textit{proxy-based} methods on DML focus on reducing the distance between similar samples while expanding the distance of dissimilar ones. However, we reveal that shrinking the distance between similar samples may distort the feature space, increasing the distance between points of the same class region and, therefore, harming the generalization of the model. Traditional regularization terms (such as $L_2$-norm on weights) cannot be adopted to solve this issue as they are based on linear projection. To alleviate this issue, we adopt the structure of normalizing flow as the deep metric layer and calculate the determinant of the Jacobi Matrix as the regularization term. At last, we conduct experiments on several \textit{pair-based} and \textit{proxy-based} algorithms that demonstrate the benefits of our method.

