On the Stochasticity in Graph Neural Networks
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Keywords: Graph Neural Networks, Variational Inference
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TL;DR: Stochasticity in GNNs remedies over-smoothing, over-squashing, and affords expressiveness exceeding the WL test.
Abstract: Graph neural networks (GNNs) that aggregate and transform point masses as \textit{messages} manifest a wide array of symptoms including limited expressiveness, over-smoothing, and over-squashing.
When stochasticity is injected into the structure of the graph, these problems can be jointly remedied, as shown in the unifying framework herein, which theoretically justifies the superior performance of a number of GNN architectures that incorporate random regularization.
For the first time, we discover that simple GNNs can \textit{exceed} the power of the Weisfeiler-Lehman test when equipped with structural stochasticity.
With insights drawn from the theoretical arguments, we design a principled way to quantify the structural uncertainty in GNNs via variational inference, termed Bayesian Rewiring of Node Networks (BRONX), and showcase its competitive performance with real-world experiments.
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Submission Number: 3832
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