GEM: A Dual-Scale Architecture for Graph-Level Hierarchical Representation Learning

Real-world networks typically exhibit small-world properties: dense local clustering yet efficient global propagation. However, current methods struggle to reconcile this hierarchy: Graph Neural Networks (GNNs) suffer from over-smoothing in long-range modeling, while sequence/state-space models often lack the inductive bias to preserve complex graph topology. To bridge this gap, we propose Graph Encoding Mamba (GEM), a dual-scale architecture for graph-level hierarchical representation learning. First, GEM employs a dual-branch encoder that synergizes the local sensitivity of GNNs with the selective scanning of Mamba, effectively capturing both local topology and global shortcuts. Second, a modularity-aware hierarchical pooling mechanism is designed to retain salient community structures during graph coarsening. Crucially, to mitigate structural redundancy from multi-scale fusion, we incorporate an Information Bottleneck objective to distill task-relevant structural patterns from redundant features, encouraging compact, task-relevant representations and supporting intrinsic interpretability. Extensive experiments on graph-level benchmarks demonstrate that GEM improves performance across biological, social, and brain network datasets. We further provide a lightweight node-level adaptation on long-range benchmarks as a boundary analysis of GEM's transferability. Code is available at \url{https://anonymous.4open.science/r/GEM-C34D}.