Hierarchical Graph Representation Learning with Pooling-Induced Substructures

Hierarchical graph-level tasks that require reasoning over substructures that extend beyond local neighborhoods are posing challenges for standard Graph Neural Networks (GNNs). While graph pooling aims to address this by coarsening graphs into hierarchical representations, existing methods often fail to explicitly preserve the substructures they induce, leading to inconsistent empirical performance. Moreover, the evaluation of such approaches has proved difficult due to the lack of benchmarks with explicit hierarchical structure. We propose Pooled-Substructure-Aware GNNs, an approach to graph pooling that explicitly preserves and processes substructures uncovered by structure-based pooling schemes. We show that this design strengthens pooling in terms of Weisfeiler-Lehman (WL) expressivity. To enable principled evaluation of pooling-based models, we introduce two new synthetic datasets with controllable hierarchical structure and propose a metric to characterize the extent of hierarchical patterns in real-world graph-level benchmarks. On tasks with relevant hierarchical structure, our approach outperforms matched pooling baselines, while remaining competitive on structurally simpler benchmarks.