Shaping Deep Feature Space Towards Gaussian Mixture for Visual Classification.

The softmax cross-entropy loss function has been widely used to train deep models for various tasks. In this work, we propose a Gaussian mixture (GM) loss function for deep neural networks for visual classification. Unlike the softmax cross-entropy loss, our method explicitly shapes the deep feature space towards a Gaussian Mixture distribution. With a classification margin and a likelihood regularization, the GM loss facilitates both high classification performance and accurate modeling of the feature distribution. The GM loss can be readily used to distinguish the adversarial examples based on the discrepancy between feature distributions of clean and adversarial examples. Furthermore, theoretical analysis shows that a symmetric feature space can be achieved by using the GM loss, which enables the models to perform robustly against adversarial attacks. The proposed model can be implemented easily and efficiently without introducing more trainable parameters. Extensive evaluations demonstrate that the method with the GM loss performs favorably on image classification, face recognition, and detection as well as recognition of adversarial examples generated by various attacks.