Almost Surely Asymptotically Constant Graph Neural Networks

• URL: http://arxiv.org/abs/2403.03880v2
• Date: Thu, 23 May 2024 15:03:45 GMT
• Title: Almost Surely Asymptotically Constant Graph Neural Networks
• Authors: Sam Adam-Day, Michael Benedikt, İsmail İlkan Ceylan, Ben Finkelshtein,
• Abstract summary: We show that the output converges to a constant function, which upper-bounds what these classifiers can uniformly express. Results apply to a broad class of random graph models. We empirically validate these findings, observing that the convergence phenomenon appears not only on random graphs but also on some real-world graphs.
• Score: 7.339728196535312
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a new angle on the expressive power of graph neural networks (GNNs) by studying how the predictions of a GNN probabilistic classifier evolve as we apply it 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 Erd\H{o}s-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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