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.

翻译：在过去的几年中，在全监督语义分割的背景下，交叉熵损失和骰子损失等若干损失函数已成为监督神经网络的事实标准。骰子损失是一个有趣的特例，因为它源自广受欢迎的骰子系数（医学影像应用中的主要评估指标之一）的松弛形式。本文首先从理论上研究骰子损失的梯度，表明其具体表现为真实值的加权负值，且动态范围非常小。这使我们能够在论文的第二部分，通过网络输出与真实值负值的简单逐元素乘法，来模拟骰子损失的监督效果。这一相当令人惊讶的结果揭示了骰子损失在梯度下降过程中实际执行的监督机制，有助于从业者理解和解释结果，同时为研究者设计新损失函数提供指导。