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This is accomplished by a Riemannian gradient flow on the manifold of parameters that determines the regularization properties of the assignment flow. Using the symplectic partitioned Runge\u2013Kutta 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.<\/jats:p>","DOI":"10.1007\/s10851-020-00977-2","type":"journal-article","created":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T01:02:56Z","timestamp":1596675776000},"page":"186-215","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Learning Adaptive Regularization for Image Labeling Using Geometric Assignment"],"prefix":"10.1007","volume":"63","author":[{"given":"Ruben","family":"H\u00fchnerbein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabrizio","family":"Savarino","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefania","family":"Petra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Schn\u00f6rr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,8,6]]},"reference":[{"key":"977_CR1","volume-title":"Methods of Information Geometry","author":"SI Amari","year":"2000","unstructured":"Amari, S.I., Nagaoka, H.: Methods of Information Geometry. 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