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

arXiv: https://arxiv.org/abs/2607.27767 · HTML: https://mlsanity.com/paper/2607.27767/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 53 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [Network Geometry](https://mlsanity.com/paper/2001.03241/) (2020)
- [Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space](https://mlsanity.com/paper/1602.06522/) (2016)
- [Graph coarsening: From scientific computing to machine learning](https://mlsanity.com/paper/2106.11863/) (2021)
- [Mercator: uncovering faithful hyperbolic embeddings of complex networks](https://mlsanity.com/paper/1904.10814/) (2019)
- [A Metadata-Driven Approach to Understand Graph Neural Networks](https://mlsanity.com/paper/2310.19263/) (2023)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [Graph Coarsening with Message-Passing Guarantees](https://mlsanity.com/paper/2405.18127/) (2024)
- [Scale-free Networks Well Done](https://mlsanity.com/paper/1811.02071/) (2018)
- [Detecting the ultra low dimensionality of real networks](https://mlsanity.com/paper/2110.14507/) (2021)
- [Geometry-Aware Edge Pooling for Graph Neural Networks](https://mlsanity.com/paper/2506.11700/) (2025)
- [Geometric renormalization unravels self-similarity of the multiscale human connectome](https://mlsanity.com/paper/1904.11793/) (2019)
- [Feature-aware ultra-low dimensional reduction of real networks](https://mlsanity.com/paper/2401.09368/) (2024)
- [Performance Heterogeneity in Graph Neural Networks: Lessons for Architecture Design and Preprocessing](https://mlsanity.com/paper/2503.00547/) (2025)

## Abstract (arXiv)

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.