A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNs
Jiaqi Wang, Xinyi Wu, James Cheng, Yifei Wang
TL;DR
The paper reinterprets oversmoothing in deep GNNs through signed graph dynamics, showing that many mitigation techniques effectively inject negative edges, whose strength and organization critically shape long-term propagation. It identifies structural balance as an ideal condition that yields stable, cluster-preserving representations and proposes Structural Balanced Propagation SBP, with Label-SBP and Feature-SBP variants to explicitly enforce balance. The approach demonstrates strong, consistent improvements across nine benchmarks including homophilic and heterophilic graphs, and remains effective up to 300 layers, while offering scalable variants for large graphs. The work provides a theoretical basis for signed message passing and offers a practical, plug-and-play method that complements existing GNN architectures. Overall, SBP advances a principled pathway to counter oversmoothing by engineering signed graph structures grounded in structural balance.
Abstract
Deep graph neural networks (GNNs) often suffer from oversmoothing, where node representations become overly homogeneous with increasing depth. While techniques like normalization, residual connections, and edge dropout have been proposed to mitigate oversmoothing, they are typically developed independently, with limited theoretical understanding of their underlying mechanisms. In this work, we present a unified theoretical perspective based on the framework of signed graphs, showing that many existing strategies implicitly introduce negative edges that alter message-passing to resist oversmoothing. However, we show that merely adding negative edges in an unstructured manner is insufficient-the asymptotic behavior of signed propagation depends critically on the strength and organization of positive and negative edges. To address this limitation, we leverage the theory of structural balance, which promotes stable, cluster-preserving dynamics by connecting similar nodes with positive edges and dissimilar ones with negative edges. We propose Structural Balanced Propagation (SBP), a plug-and-play method that assigns signed edges based on either labels or feature similarity to explicitly enhance structural balance in the constructed signed graphs. Experiments on nine benchmarks across both homophilic and heterophilic settings demonstrate that SBP consistently improves classification accuracy and mitigates oversmoothing, even at depths of up to 300 layers. Our results provide a principled explanation for prior oversmoothing remedies and introduce a new direction for signed message-passing design in deep GNNs.