Graph Neural Networks (GNNs) have achieved remarkable success across a range of learning tasks. However, scaling GNNs to large graphs remains a significant challenge, especially for graph-level tasks. In this work, we introduce SHAKE-GNN, a novel scalable graph-level GNN framework based on a hierarchy of Kirchhoff Forests, a class of random spanning forests used to construct stochastic multi-resolution decompositions of graphs. SHAKE-GNN produces multi-scale representations, enabling flexible trade-offs between efficiency and performance. We introduce an improved, data-driven strategy for selecting the trade-off parameter and analyse the time-complexity of SHAKE-GNN. Experimental results on multiple large-scale graph classification benchmarks demonstrate that SHAKE-GNN achieves competitive performance while offering improved scalability.
@article{arxiv.2509.22100,
title = {SHAKE-GNN: Scalable Hierarchical Kirchhoff-Forest Graph Neural Network},
author = {Zhipu Cui and Johannes Lutzeyer},
journal= {arXiv preprint arXiv:2509.22100},
year = {2025}
}