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The performance of GNNs degrades as they become deeper due to theover-smoothing. Among all the attempts to prevent over-smoothing, residualconnection is one of the promising methods due to its simplicity. However,recent studies have shown that GNNs with residual connections only slightlyslow down the degeneration. The reason why residual connections fail in GNNs isstill unknown. In this paper, we investigate the forward and backward behaviorof GNNs with residual connections from a novel path decomposition perspective.We find that the recursive aggregation of the median length paths from thebinomial distribution of residual connection paths dominates outputrepresentation, resulting in over-smoothing as GNNs go deeper. Entangledpropagation and weight matrices cause gradient smoothing and prevent GNNs withresidual connections from optimizing to the identity mapping. Based on thesefindings, we present a Universal Deep GNNs (UDGNN) framework with cold-startadaptive residual connections (DRIVE) and feedforward modules. Extensiveexperiments demonstrate the effectiveness of our method, which achievesstate-of-the-art results over non-smooth heterophily datasets by simplystacking standard GNNs.

Universal Deep GNNs: Rethinking Residual Connection in GNNs from a Path Decomposition Perspective for Preventing the Over-smoothing