Deep assignment flows for structured data labeling: design, learning and prediction performance

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This project focuses on a class of continuous-time neural ordinary differential equations (nODEs) for labeling metric data on graphs, in order to contribute to the theory of deep learning from three viewpoints: (i) use of information geometry for design and understanding the role of parameters in connection with learning and structured prediction; (ii) study of PAC-Bayes risk bounds for local predictions of weight parameter patches on a manifold and the implication for the statistical accuracy of non-local labelings predicted by the nODE; (iii) algorithm design for parameter learning based on a linear tangent space representation of the nODE, as a basis for linking statistical learning theory to applications of assignment flows in practice.