arXiv:2611.14126v1 Announce Type: new Abstract: 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, evaluating such approaches remains challenging 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 enhances the expressive power of pooling-based GNNs in the sense of the Weisfeiler-Lehman (WL) test. To enable principled evaluation, we introduce two new synthetic datasets with controllable hierarchical structure and propose a metric to characterize the prevalence 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. Code and datasets are publicly available at https://github.com/lsbicego/PSA-GNN/.