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Deep learning has become the method of choice in many application domains ofmachine learning in recent years, especially for multi-class classificationtasks. The most common loss function used in this context is the cross-entropyloss, which reduces to the log loss in the typical case when there is a singlecorrect response label. While this loss is insensitive to the identity of theassigned class in the case of misclassification, in practice it is often thecase that some errors may be more detrimental than others. Here we present thebilinear-loss (and related log-bilinear-loss) which differentially penalizesthe different wrong assignments of the model. We thoroughly test this methodusing standard models and benchmark image datasets. As one application, we showthe ability of this method to better contain error within the correctsuper-class, in the hierarchically labeled CIFAR100 dataset, without affectingthe overall performance of the classifier.

Every Untrue Label is Untrue in its Own Way: Controlling Error Type with the Log Bilinear Loss