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 abnormal inputs, such as the adversarial examples, based on the discrepancy between feature distributions of the inputs and the training set. 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 using extra trainable parameters. Extensive evaluations demonstrate that the proposed method performs favorably not only on image classification but also on robust detection of adversarial examples generated by strong attacks under different threat models.