Pseudo-Graph Neural Networks On Ordinary Differential Equations

Abstract

In this paper, we extend the idea of continuous-depth models to pseudo graphs and present pseudo graph ordinary differential equations (PGODE), which are inspired by the neural ordinary differential equation (NODE) for data in the Euclidean domain. All existing graph networks have discrete depth. A pseudo graph neural network (PGNN) is used to parameterize the derivative of hidden node states, and the output states are the solution to this ordinary differential equation (ODE). A memory-efficient framework with precise gradient estimates is then proposed for free-form ODEs. We also introduce the framework of continuous–depth pseudo graph neural networks (PGNNs) on ODE by blending discrete structures and differential equations