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Statistical Mechanics of Generalization In Graph Convolution Networks

Cheng ShiLiming PanHong HuIvan Dokmani\'c
Dec 2022
摘要
Graph neural networks (GNN) have become the default machine learning modelfor relational datasets, including protein interaction networks, biologicalneural networks, and scientific collaboration graphs. We use tools fromstatistical physics and random matrix theory to precisely characterizegeneralization in simple graph convolution networks on the contextualstochastic block model. The derived curves are phenomenologically rich: theyexplain the distinction between learning on homophilic and heterophilic graphsand they predict double descent whose existence in GNNs has been questioned byrecent work. Our results are the first to accurately explain the behavior notonly of a stylized graph learning model but also of complex GNNs on messyreal-world datasets. To wit, we use our analytic insights about homophily andheterophily to improve performance of state-of-the-art graph neural networks onseveral heterophilic benchmarks by a simple addition of negative self-loopfilters.
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