  In deep neural network, the cross-entropy loss function is commonly used for
classification. Minimizing cross-entropy is equivalent to maximizing likelihood
under assumptions of uniform feature and class distributions. It belongs to
generative training criteria which does not directly discriminate correct class
from competing classes. We propose a discriminative loss function with negative
log likelihood ratio between correct and competing classes. It significantly
outperforms the cross-entropy loss on the CIFAR-10 image classification task.
