Train Small, Deploy Large: Zero-Shot GNN Transfer Across Graph Scales

Graph neural networks (GNNs) can operate on graphs of different sizes, yet weights learned at one resolution do not necessarily remain effective at another. We investigate whether training on a smaller replica allows zero-shot deployment on the full-resolution graph. We construct these replicas using geometric renormalization (GR), a previously proposed scale transformation designed to preserve latent geometry and self-similar multiscale organization. Across synthetic networks and eight real-world node-classification datasets, GCN, GraphSAGE, and GAT models trained on graphs compressed by factors up to 32 often retain much of the full-resolution accuracy while reducing training cost. Matched-compression randomization controls show that this effect cannot be explained by graph-size reduction alone: randomizing topology, latent geometry, or both breaks the relation between scales and substantially weakens transfer. CKA and orthogonal Procrustes analyses reveal cross-scale alignment of learned representations, while Jensen–Shannon comparisons show similar predictive trajectories during training. Comparisons with established coarsening methods show that GR remains competitive in transfer accuracy while generally preserving measured structural properties more faithfully. Together, these results identify self-similarity as a structural basis for cross-scale GNN transfer and position GR as a reusable training surrogate and controlled framework for studying cross-scale learning in graphs.