Graph Element Networks: adaptive, structured computation and memory
This work addresses spatial modeling challenges in fields like robotics and computer vision, offering an adaptive, structured approach, but it is incremental as it builds on existing GNN methods.
The paper tackles the problem of modeling spatial processes without predefined graphical structures by using graph neural networks (GNNs) as a computational substrate, showing that node locations and connectivity can be optimized to focus on complex spatial regions, and demonstrating generalization over space size and precision trade-offs in PDE, robotics, and scene prediction tasks.
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined on the graph to model the relationship between an initial function defined over a space and a resulting function in the same space. We use GNNs as a computational substrate, and show that the locations of the nodes in space as well as their connectivity can be optimized to focus on the most complex parts of the space. Moreover, this representational strategy allows the learned input-output relationship to generalize over the size of the underlying space and run the same model at different levels of precision, trading computation for accuracy. We demonstrate this method on a traditional PDE problem, a physical prediction problem from robotics, and learning to predict scene images from novel viewpoints.