PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations
This addresses the performance degradation in deep graph networks for applications like computer vision and computational biology, offering a novel solution to a known bottleneck.
The paper tackles the over-smoothing problem in deep graph neural networks by proposing PDE-GCN, a family of architectures motivated by numerical methods for solving partial differential equations, which achieves better or on-par state-of-the-art results across various fields.
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.