Almost Surely Asymptotically Constant Graph Neural Networks

Code

• github.com/benfinkelshtein/gnn-asymptotically-constant
  OfficialIn paperpytorch★ 3

Abstract

We present a new angle on the expressive power of graph neural networks (GNNs) by studying how the predictions of real-valued GNN classifiers, such as those classifying graphs probabilistically, evolve as we apply them on larger graphs drawn from some random graph model. We show that the output converges to a constant function, which upper-bounds what these classifiers can uniformly express. This strong convergence phenomenon applies to a very wide class of GNNs, including state of the art models, with aggregates including mean and the attention-based mechanism of graph transformers. Our results apply to a broad class of random graph models, including sparse and dense variants of the Erdos-R\'enyi model, the stochastic block model, and the Barab\'asi-Albert model. We empirically validate these findings, observing that the convergence phenomenon appears not only on random graphs but also on some real-world graphs.

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Reproductions