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Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks

NeurIPS

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Published on

12/04/2022

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NeurIPS

Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be simulated by GNNs. However, those simulations involve neural networks for the “combine” function of size polynomial or even exponential in the number of graph nodes n, as well as feature vectors of length linear in n. We present an improved simulation of the WL test on GNNs with exponentially lower complexity. In particular, the neural network implementing the combine function in each node has only polylog(n) parameters, and the feature vectors exchanged by the nodes of GNN consists of only O(log n) bits. We also give logarithmic lower bounds for the feature vector length and the size of the neural networks, showing the (near)-optimality of our construction.

Please cite our work using the BibTeX below.

@inproceedings{
aamand2022exponentially,
title={Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks},
author={Anders Aamand and Justin Y Chen and Piotr Indyk and Shyam Narayanan and Ronitt Rubinfeld and Nicholas Schiefer and Sandeep Silwal and Tal Wagner},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=AyGJDpN2eR6}
}
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