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We investigate size-induced distribution shifts in graphs and assess theirimpact on the ability of graph neural networks (GNNs) to generalize to largergraphs relative to the training data. Existing literature presents conflictingconclusions on GNNs' size generalizability, primarily due to disparities inapplication domains and underlying assumptions concerning size-induceddistribution shifts. Motivated by this, we take a data-driven approach: wefocus on real biological datasets and seek to characterize the types ofsize-induced distribution shifts. Diverging from prior approaches, we adopt aspectral perspective and identify that spectrum differences induced by size arerelated to differences in subgraph patterns (e.g., average cycle lengths). Wefurther find that common GNNs cannot capture these subgraph patterns, resultingin performance decline when testing on larger graphs. Based on these spectralinsights, we introduce and compare three model-agnostic strategies aimed atmaking GNNs aware of important subgraph patterns to enhance their sizegeneralizability: self-supervision, augmentation, and size-insensitiveattention. Our empirical results reveal that all strategies enhance GNNs' sizegeneralizability, with simple size-insensitive attention surprisingly emergingas the most effective method. Notably, this strategy substantially enhancesgraph classification performance on large test graphs, which are 2-10 timeslarger than the training graphs, resulting in an improvement in F1 scores by upto 8%.

Size Generalization of Graph Neural Networks on Biological Data: Insights and Practices from the Spectral Perspective