How Powerful are Graph Neural Networks with Random Weights?
Keywords: Graph Neural Networks, Graph Isomorphism, Neighborhood Aggregation, Graph Classification
Abstract: Thanks to the great success of graph neural networks (GNNs) in structural information learning, extensive variants by virtue of sampling or pooling have been developed to further improve the performance, scalability, and applicability. However, there is still room for improvement in learning efficiency because current GNNs are trained via batch gradient descent with many graphs in each iteration. The good potential of random features in speeding up the training phase motivates us to consider the expressive power of GNNs with random weights. Based on the framework of Graph Isomorphism Network, we propose a novel model called Hashing Graph Isomorphism Network (HashGIN) with only one epoch of training by revising the convolutional layer with random hash functions and adjusting the learning objective with regularized least squares loss. In light of the property of $k$ random hash functions, we theoretically show that the injective phase in the Weisfeiler-Lehman test can be approximated by a hash family. An approximation upper bound is further provided with rigorous mathematical proof for the convergence of our model. Our experiments on several benchmark datasets show that HashGIN is effective and efficient for graph classification tasks. Compared to the state-of-the-art methods, HashGIN achieves better or comparable accuracies with less training time and memory cost.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 2210
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