2022/11/06 by Anders Aamand, Justin Y. Chen, Aamand, Anders +13 · 1 citation
Computer Science · #Advanced Graph Neural Networks #Adversarial Robustness in Machine Learning #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2211.03232
openalex publication_date 2022/11/06 · openalex created_date 2022/11/13 · openalex updated_date 2026/07/28
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 a polylogarithmic number of parameters in n, 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.