A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNs

TL;DR

This paper introduces a unified theoretical framework using signed graphs to understand and mitigate oversmoothing in deep GNNs, proposing a new method called Structural Balanced Propagation that improves performance across various benchmarks.

Contribution

It provides a theoretical perspective linking oversmoothing mitigation to signed graph theory and introduces SBP, a practical method leveraging structural balance for deep GNNs.

Findings

SBP improves accuracy across nine benchmarks.

SBP effectively mitigates oversmoothing at depths up to 300 layers.

Theoretical insights connect oversmoothing remedies to signed graph principles.

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.