SHAKE-GNN: Scalable Hierarchical Kirchhoff-Forest Graph Neural Network

Zhipu Cui; Johannes Lutzeyer

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arXiv · 2509.22100

SHAKE-GNN: Scalable Hierarchical Kirchhoff-Forest Graph Neural Network

Zhipu Cui·Johannes Lutzeyer

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Abstract

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.

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Zhipu Cui, Johannes Lutzeyer. 2026-08-29. SHAKE-GNN: Scalable Hierarchical Kirchhoff-Forest Graph Neural Network. https://arxiv.org/abs/2509.22100

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