  Deep learning has become the method of choice in many application domains of
machine learning in recent years, especially for multi-class classification
tasks. The most common loss function used in this context is the cross-entropy
loss, which reduces to the log loss in the typical case when there is a single
correct response label. While this loss is insensitive to the identity of the
assigned class in the case of misclassification, in practice it is often the
case that some errors may be more detrimental than others. Here we present the
bilinear-loss (and related log-bilinear-loss) which differentially penalizes
the different wrong assignments of the model. We thoroughly test this method
using standard models and benchmark image datasets. As one application, we show
the ability of this method to better contain error within the correct
super-class, in the hierarchically labeled CIFAR100 dataset, without affecting
the overall performance of the classifier.
