  The Sinkhorn operator has recently experienced a surge of popularity in
computer vision and related fields. One major reason is its ease of integration
into deep learning frameworks. To allow for an efficient training of respective
neural networks, we propose an algorithm that obtains analytical gradients of a
Sinkhorn layer via implicit differentiation. In comparison to prior work, our
framework is based on the most general formulation of the Sinkhorn operator. It
allows for any type of loss function, while both the target capacities and cost
matrices are differentiated jointly. We further construct error bounds of the
resulting algorithm for approximate inputs. Finally, we demonstrate that for a
number of applications, simply replacing automatic differentiation with our
algorithm directly improves the stability and accuracy of the obtained
gradients. Moreover, we show that it is computationally more efficient,
particularly when resources like GPU memory are scarce.
