Edge-conditioned Markov kernels for stable label refinement on heterophilous graphs

초록

Graph neural networks often exhibit degraded performance on heterophilous graphs because neighborhood aggregation implicitly assumes label similarity and can amplify misleading sig nals. To address this issue, we propose a probabilistic and stable label refinement framework that decouples feature encoding from graph-driven inference. We refer to the resulting model as Edge-conditioned Markov Stable Refinement (EMSR). First, an encoder produces base unary logits from node features. Then, we assign each directed edge an edge-conditioned Markov kernel to cap ture mixed homophily and heterophily. Each kernel is constructed as a mixture over a small set of row-stochastic class-transition templates, with the identity as a strict homophily special case. Final predictions are obtained by inferring a global label field on the product simplex through minimization of a convex energy. Our theoretical analysis shows that the fixed-parameter infer ence objective is strongly convex. We optimize this objective with entropic mirror descent and enforce monotonic decrease via backtracking. All components are trained end-to-end using stan dard supervision, and we evaluate our method on nine benchmark datasets spanning homophilous and heterophilous regimes. Our code is available at https://github.com/ChoiYoonHyuk/EMSR.

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