  This paper builds on the connection between graph neural networks and
traditional dynamical systems. We propose continuous graph neural networks
(CGNN), which generalise existing graph neural networks with discrete dynamics
in that they can be viewed as a specific discretisation scheme. The key idea is
how to characterise the continuous dynamics of node representations, i.e. the
derivatives of node representations, w.r.t. time. Inspired by existing
diffusion-based methods on graphs (e.g. PageRank and epidemic models on social
networks), we define the derivatives as a combination of the current node
representations, the representations of neighbors, and the initial values of
the nodes. We propose and analyse two possible dynamics on graphs---including
each dimension of node representations (a.k.a. the feature channel) change
independently or interact with each other---both with theoretical
justification. The proposed continuous graph neural networks are robust to
over-smoothing and hence allow us to build deeper networks, which in turn are
able to capture the long-range dependencies between nodes. Experimental results
on the task of node classification demonstrate the effectiveness of our
proposed approach over competitive baselines.
