Optimization of Graph Neural Networks: Implicit Acceleration by Skip Connections and More Depth

• URL: http://arxiv.org/abs/2105.04550v1
• Date: Mon, 10 May 2021 17:59:01 GMT
• Title: Optimization of Graph Neural Networks: Implicit Acceleration by Skip Connections and More Depth
• Authors: Keyulu Xu, Mozhi Zhang, Stefanie Jegelka, Kenji Kawaguchi
• Abstract summary: Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. We study the dynamics of GNNs by studying deep skip optimization. Our results provide first theoretical support for the success of GNNs.
• Score: 57.10183643449905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

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