  In this work, we propose to employ information-geometric tools to optimize a
graph neural network architecture such as the graph convolutional networks.
More specifically, we develop optimization algorithms for the graph-based
semi-supervised learning by employing the natural gradient information in the
optimization process. This allows us to efficiently exploit the geometry of the
underlying statistical model or parameter space for optimization and inference.
To the best of our knowledge, this is the first work that has utilized the
natural gradient for the optimization of graph neural networks that can be
extended to other semi-supervised problems. Efficient computations algorithms
are developed and extensive numerical studies are conducted to demonstrate the
superior performance of our algorithms over existing algorithms such as ADAM
and SGD.
