Better Not to Propagate: Understanding Edge Uncertainty and Over-smoothing in Signed Graph Neural Networks

Traditional Graph Neural Networks (GNNs) rely on network homophily, which can lead to performance degradation due to over-smoothing in many real-world heterophily scenarios. Recent studies analyze the smoothing effect (separability) after message-passing (MP), depending on the expectation of node features. Regarding separability gain, they provided theoretical backgrounds on over-smoothing caused by various propagation schemes, including positive, signed, and blocked MPs. More recently, by extending these theorems, some works have suggested improvements in signed propagation under multiple classes. However, prior works assume that the error ratio of all propagation schemes is fixed, failing to investigate this phenomenon correctly. To solve this problem, we propose a novel method for estimating homophily and edge error ratio, integrated with dynamic selection between blocked and signed propagation during training. Our theoretical analysis, supported by extensive experiments, demonstrates that blocking MP can be more effective than signed propagation under high edge error ratios, improving the performance in both homophilic and heterophilic graphs.