Optimal community detection with graphical neural networks

ICLR 2026 Conference Submission18558 Authors

Keywords: Graphical Neural Networks (GNNs), Community Detection, Minimax optimality, Stochastic Blockmodels (SBM), Supervised learning

TL;DR: The paper shows a two-stage GNN framework achieves minimax optimality for community detection, matching classical methods, and works off-the-shelf with strong empirical performance and theoretical guarantees.

Abstract: This paper investigates the theoretical optimality of community detection in networks using graph neural networks (GNNs). We show that appropriately designed GNNs for supervised community detection can match the performance of classical spectral and likelihood-based methods, achieving information-theoretic optimality under the stochastic block model. These results provide the first rigorous connection between deep learning algorithms and their statistical guarantees for community detection. We extend existing GNN-based methods into a two-stage framework, where the second stage is critical for ensuring theoretical optimality. Our algorithm is trained on synthetic and/or real-world graphs with known community labels and can be subsequently applied as generic algorithms to any network in an off-the-shelf manner, offering strong practicality. Extensive experiments on both synthetic and real-world datasets support our theoretical findings, demonstrating that the proposed two-stage GNN framework delivers high accuracy and remains robust under model mis-specification. These results establish GNNs as both a theoretically sound and practically effective approach to community detection.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 18558