Selective blocking for message-passing neural networks on heterophilic graphs

초록

Graph Neural Networks (GNNs) thrive on message passing (MP) but are vulnerable when the graph carries many heterophilic or misclassified edges. Prior analyses suggest that signed propagation can mitigate over-smoothing under low edge–error rates, yet they implicitly assume perfect edge labels and the presence of self-loops. We revisit this setting and show that, under high edge uncertainty, propagating any information may harm node separability even with signed weights. Our key insight is to decide not to propagate along uncertain edges adaptively. Concretely, we intentionally omit self-loops to isolate pure neighbor influence for a clearer theoretical analysis, adopt a row-stochastic (asymmetric) operator that matches the Markov–chain view of MP and simplifies spectral-radius proofs. Then, we dynamically estimate the local homophily bi and edge-classification error et during training via an EM procedure. We prove that our selective blocking yields a sub-stochastic propagation matrix whose joint spectral radius exceeds that of signed GNNs under high et, guaranteeing reduced over-smoothing, and we supply a lemma showing that class-discriminative signals survive even when the operator is rank-deficient. Extensive experiments on six homophilic and heterophilic benchmarks confirm that the proposed adaptive blocking outperforms strong baselines.