Selective Blocking for Message-Passing Neural Networks on Heterophilic Graphs

Yoonhyuk Choi, Taewook Ko, Jiho Choi, Chong-Kwon Kim

Keywords: Graph neural network, graph heterophily, edge uncertainty, oversmoothing

TL;DR: We propose a novel method for estimating homophily and edge error ratios, along with a dynamic selection mechanism between blocked and signed propagation during training

Abstract: 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, and dynamically estimate the local homophily $b_i$ and edge‑classification error $e_t$ 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 $e_t$, 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 seven homophilic and heterophilic benchmarks confirm that the proposed adaptive blocking outperforms strong baselines.

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission3/Authors, auai.org/UAI/2025/Conference/Submission3/Reproducibility_Reviewers

Submission Number: 3