PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations

Moshe Eliasof, Eldad Haber, Eran Treister

Keywords: Graph Neural Networks, Neural Network Architectures, PDES in Deep Learning, Partial Differential Equations

TL;DR: We propose a novel PDE-motivated family of GCN architectures that prevent over-smoothing and obtain state-of-the-art results, backed up by theoretical guarantees.

Abstract:

Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional neural networks, deep graph networks do not necessarily yield better performance than shallow graph networks.
This behavior usually stems from the over-smoothing phenomenon. In this work, we propose a family of architectures
to control this behavior by design. Our networks are motivated by numerical methods for solving Partial Differential Equations (PDEs) on manifolds, and as such, their behavior can be explained by similar analysis. Moreover, as we demonstrate using an extensive set of experiments, our PDE-motivated networks can generalize and be effective for various types of problems from different fields. Our architectures obtain better or on par with the current state-of-the-art results for problems that are typically approached using different architectures.

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