  During the training process, deep neural networks implicitly learn to
represent the input data samples through a hierarchy of features, where the
size of the hierarchy is determined by the number of layers. In this paper, we
focus on enforcing the discriminative power of the high-level representations,
that are typically learned by the deeper layers (closer to the output). To this
end, we introduce a new loss term inspired by the Gini impurity, which is aimed
at minimizing the entropy (increasing the discriminative power) of individual
high-level features with respect to the class labels. Although our Gini loss
induces highly-discriminative features, it does not ensure that the
distribution of the high-level features matches the distribution of the
classes. As such, we introduce another loss term to minimize the
Kullback-Leibler divergence between the two distributions. We conduct
experiments on two image classification data sets (CIFAR-100 and Caltech 101),
considering multiple neural architectures ranging from convolutional networks
(ResNet-17, ResNet-18, ResNet-50) to transformers (CvT). Our empirical results
show that integrating our novel loss terms into the training objective
consistently outperforms the models trained with cross-entropy alone, without
increasing the inference time at all.
