We propose a large-margin Gaussian Mixture (L-GM) loss for deep neural networks in classification tasks. Different from the softmax cross-entropy loss, our proposal is established on the assumption that the deep features of the training set follow a Gaussian Mixture distribution. By involving a classification margin and a likelihood regularization, the L-GM loss facilitates both a high classification performance and an accurate modeling of the training feature distribution. As such, the L-GM loss is superior to the softmax loss and its major variants in the sense that besides classification, it can be readily used to distinguish abnormal inputs, such as the adversarial examples, based on their features' likelihood to the training feature distribution. Extensive experiments on various recognition benchmarks like MNIST, CIFAR, ImageNet and LFW, as well as on adversarial examples demonstrate the effectiveness of our proposal.

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Plenty of effective methods have been proposed for face recognition during the past decade. Although these methods differ essentially in many aspects, a common practice of them is to specifically align the facial area based on the prior knowledge of human face structure before feature extraction. In most systems, the face alignment module is implemented independently. This has actually caused difficulties in the designing and training of end-to-end face recognition models. In this paper we study the possibility of alignment learning in end-to-end face recognition, in which neither prior knowledge on facial landmarks nor artificially defined geometric transformations are required. Specifically, spatial transformer layers are inserted in front of the feature extraction layers in a Convolutional Neural Network (CNN) for face recognition. Only human identity clues are used for driving the neural network to automatically learn the most suitable geometric transformation and the most appropriate facial area for the recognition task. To ensure reproducibility, our model is trained purely on the publicly available CASIA-WebFace dataset, and is tested on the Labeled Face in the Wild (LFW) dataset. We have achieved a verification accuracy of 99.08% which is comparable to state-of-the-art single model based methods.