Computer Science > Machine Learning
[Submitted on 4 Aug 2021 (v1), last revised 26 Oct 2021 (this version, v2)]
Title:PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations
View PDFAbstract: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.
Submission history
From: Moshe Eliasof [view email][v1] Wed, 4 Aug 2021 09:59:57 UTC (6,412 KB)
[v2] Tue, 26 Oct 2021 20:03:19 UTC (2,968 KB)
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