n‑HDP‑GNN: community‑aware Bayesian clustering for over‑smoothing‑resilient, communication‑efficient distributed GNNs

Abstract Deep graph neural networks (GNNs) often suffer from over‑smoothing, where node embeddings homogenize as depth grows. We present n‑HDP‑GNN, a probabilistic, community‑aware architecture that couples Louvain coarsening with a nested Hierarchical Dirichlet process to learn soft responsibilities that gate message passing. Multi‑level attention (node/community/global) then aggregates features while preserving separability. This selective diffusion delays over‑smoothing—quantified once using MADGap—and, in distributed training, reduces cross‑partition communication by lowering the cross‑partition edge ratio and increasing edge‑reduction. We evaluate across seven benchmarks spanning citation networks, a co‑purchase network, and three large‑scale tasks, under supervised, semi‑supervised, and label‑scarce regimes, against strong baselines. The proposed model delivers over 5% gain in accuracy, greater robustness, and a superior ability to capture long‑range dependencies and subtle patterns. Deployed on a multi‑node CPU cluster with PyTorch DDP, n‑HDP‑GNN attains + 11% higher throughput than the best competitor at matched accuracy, demonstrating that the same community‑aware gating curbs over‑smoothing and improves communication efficiency on commodity interconnects. Together, these results show that probabilistic, community‑aware gating yields depth‑robust representations without sacrificing scalability: mid‑depth performance is strengthened, deep‑depth degradation is reduced, and systems metrics improve in tandem turning a representation‑level idea into a practical approach for training deep GNNs on modest clusters.