  In the past few years, in the context of fully-supervised semantic
segmentation, several losses -- such as cross-entropy and dice -- have emerged
as de facto standards to supervise neural networks. The Dice loss is an
interesting case, as it comes from the relaxation of the popular Dice
coefficient; one of the main evaluation metric in medical imaging applications.
In this paper, we first study theoretically the gradient of the dice loss,
showing that concretely it is a weighted negative of the ground truth, with a
very small dynamic range. This enables us, in the second part of this paper, to
mimic the supervision of the dice loss, through a simple element-wise
multiplication of the network output with a negative of the ground truth. This
rather surprising result sheds light on the practical supervision performed by
the dice loss during gradient descent. This can help the practitioner to
understand and interpret results while guiding researchers when designing new
losses.
