  Probabilistic theory and differential equation are powerful tools for the
interpretability and guidance of the design of machine learning models,
especially for illuminating the mathematical motivation of learning latent
variable from observation. Subspace learning maps high-dimensional features on
low-dimensional subspace to capture efficient representation. Graphs are widely
applied for modeling latent variable learning problems, and graph neural
networks implement deep learning architectures on graphs. Inspired by
probabilistic theory and differential equations, this paper conducts notes and
proposals about graph neural networks to solve subspace learning problems by
variational inference and differential equation. Source code of this paper is
available at https://github.com/zshicode/Latent-variable-GNN.
