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

该项目专注于一类用于标记图上度量数据的连续时间神经常微分方程（node），以便从三个角度为深度学习理论做出贡献：(i)使用信息几何来设计和理解参数在学习和结构化预测中的作用；（ii）研究了流形上权重参数块局部预测的PAC-Bayes风险界限，以及节点预测的非局部标记的统计准确性的含义；（iii）基于节点的线性切线空间表示的参数学习算法设计，作为将统计学习理论与分配流在实践中的应用联系起来的基础。

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.