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.

本研究提出了一种基于大边界高斯混合（L-GM）损失函数的深度神经网络分类方法，相较于常规的 softmax cross-entropy 损失函数，通过加入分类边界和似然正则化，提高了分类准确性以及对于训练特征分布的建模精度，可以用于区分异常输入如对抗性样本等。经过 MNIST、CIFAR、ImageNet 和 LFW 等基准测试和对抗性样本测试，证明了本方法的有效性。