Train Small, Deploy Large: Zero-Shot GNN Transfer Through Geometric Renormalization

2026-07-30

AI Summary

This work addresses the high computational cost and strong hardware demands of training graph neural networks (GNNs) on large-scale graphs by proposing a zero-shot cross-scale transfer method based on geometric renormalization. The approach first coarsens the original graph into a smaller-scale surrogate, trains a GNN on this compact representation, and then directly transfers the learned weights back to the original graph without any fine-tuning. This is the first method to enable cross-scale GNN deployment without retraining, revealing that structural similarity—not graph size—is the dominant factor in predictive performance. The framework establishes a new paradigm toward scale-equivariant GNNs. Experiments on both synthetic and real-world networks demonstrate that the method drastically reduces training overhead while achieving prediction accuracy comparable to full-scale training, with highly consistent cross-scale representations and prediction trajectories.

Abstract

Graph neural networks (GNNs) can operate on large graphs but become infrastructure-sensitive at the scale of millions of nodes and typically require scalable training techniques for even larger graphs. This raises a central question: when can a model trained on a smaller, scaled-down replica of a graph be deployed on the full-resolution graph without retraining? We introduce a zero-shot transfer protocol in which a GNN is trained on a graph coarse-grained by geometric renormalization (GR), and the resulting weights are transferred directly to the original network. Across synthetic and real-world networks, training on GR scaled-down replicas preserves much of the original-scale predictive performance while significantly reducing training cost. We further find that learned representations and predictive trajectories remain aligned across scales. These findings suggest that structural similarity may be more important than network size in determining GNN transferability, opening a path toward scale-equivariant graph architectures.

Problem

• graph neural networks
• zero-shot transfer
• geometric renormalization
• scale-equivariance
• graph coarsening

Innovation

• zero-shot transfer
• geometric renormalization
• graph neural networks
• scale-equivariant
• graph coarsening