  We study the inverse problem of model parameter learning for pixelwise image
labeling, using the linear assignment flow and training data with ground truth.
This is accomplished by a Riemannian gradient flow on the manifold of
parameters that determine the regularization properties of the assignment flow.
Using the symplectic partitioned Runge--Kutta method for numerical integration,
it is shown that deriving the sensitivity conditions of the parameter learning
problem and its discretization commute. A convenient property of our approach
is that learning is based on exact inference. Carefully designed experiments
demonstrate the performance of our approach, the expressiveness of the
mathematical model as well as its limitations, from the viewpoint of
statistical learning and optimal control.
