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Graph convolutional networks are a popular class of deep neural networkalgorithms which have shown success in a number of relational learning tasks.Despite their success, graph convolutional networks exhibit a number ofpeculiar features, including a bias towards learning oversmoothed andhomophilic functions, which are not easily diagnosed due to the complex natureof these algorithms. We propose to bridge this gap in understanding by studyingthe neural tangent kernel of sheaf convolutional networks--a topologicalgeneralization of graph convolutional networks. To this end, we derive aparameterization of the neural tangent kernel for sheaf convolutional networkswhich separates the function into two parts: one driven by a forward diffusionprocess determined by the graph, and the other determined by the compositeeffect of nodes' activations on the output layer. This geometrically-focusedderivation produces a number of immediate insights which we discuss in detail.

Graph Convolutional Networks from the Perspective of Sheaves and the Neural Tangent Kernel