  This paper presents an experimental analysis about trade-offs in top-k
classification accuracies on losses for deep leaning and proposal of a novel
top-k loss. Commonly-used cross entropy (CE) is not guaranteed to optimize
top-k prediction without infinite training data and model complexities. The
objective is to clarify when CE sacrifices top-k accuracies to optimize top-1
prediction, and to design loss that improve top-k accuracy under such
conditions. Our novel loss is basically CE modified by grouping temporal top-k
classes as a single class. To obtain a robust decision boundary, we introduce
an adaptive transition from normal CE to our loss, and thus call it top-k
transition loss. It is demonstrated that CE is not always the best choice to
learn top-k prediction in our experiments. First, we explore trade-offs between
top-1 and top-k (=2) accuracies on synthetic datasets, and find a failure of CE
in optimizing top-k prediction when we have complex data distribution for a
given model to represent optimal top-1 prediction. Second, we compare top-k
accuracies on CIFAR-100 dataset targeting top-5 prediction in deep learning.
While CE performs the best in top-1 accuracy, in top-5 accuracy our loss
performs better than CE except using one experimental setup. Moreover, our loss
has been found to provide better top-k accuracies compared to CE at k larger
than 10. As a result, a ResNet18 model trained with our loss reaches 99 %
accuracy with k=25 candidates, which is a smaller candidate number than that of
CE by 8.
