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

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.