  In computational pathology, cancer grading has been mainly studied as a
categorical classification problem, which does not utilize the ordering nature
of cancer grades such as the higher the grade is, the worse the cancer is. To
incorporate the ordering relationship among cancer grades, we introduce a
differential ordinal learning problem in which we define and learn the degree
of difference in the categorical class labels between pairs of samples by using
their differences in the feature space. To this end, we propose a
transformer-based neural network that simultaneously conducts both categorical
classification and differential ordinal classification for cancer grading. We
also propose a tailored loss function for differential ordinal learning.
Evaluating the proposed method on three different types of cancer datasets, we
demonstrate that the adoption of differential ordinal learning can improve the
accuracy and reliability of cancer grading, outperforming conventional cancer
grading approaches. The proposed approach should be applicable to other
diseases and problems as they involve ordinal relationship among class labels.
