  Graph convolutional networks are a popular class of deep neural network
algorithms which have shown success in a number of relational learning tasks.
Despite their success, graph convolutional networks exhibit a number of
peculiar features, including a bias towards learning oversmoothed and
homophilic functions, which are not easily diagnosed due to the complex nature
of these algorithms. We propose to bridge this gap in understanding by studying
the neural tangent kernel of sheaf convolutional networks--a topological
generalization of graph convolutional networks. To this end, we derive a
parameterization of the neural tangent kernel for sheaf convolutional networks
which separates the function into two parts: one driven by a forward diffusion
process determined by the graph, and the other determined by the composite
effect of nodes' activations on the output layer. This geometrically-focused
derivation produces a number of immediate insights which we discuss in detail.
