Interpretable and Adaptive Node Classification on Heterophilic Graphs via Combinatorial Scoring and Hybrid Learning

TL;DR

The paper tackles semi-supervised node classification across graphs with varying levels of homophily and heterophily by proposing an interpretable combinatorial inference framework that avoids deep message passing. It relies on an explicit additive scoring rule that combines global class priors, neighborhood statistics, feature-space similarity, and train-derived label–label compatibility, with a small set of hyperparameters to adapt across regimes. A validation-gated hybrid refinement injects combinatorial predictions as logit priors into a lightweight neural model, activated only when validation shows a benefit, ensuring interpretability when neural refinement is unnecessary. Experiments show competitive accuracy with modern heterophily-aware GNNs on heterophilic benchmarks while offering advantages in interpretability, computational efficiency, and leakage-free evaluation, and demonstrate adaptive behavior across transition and homophilic regimes. Overall, the approach provides a robust, transparent alternative to deep message passing that can be tuned to domain-specific requirements and deployed with fast inference once hyperparameters are fixed.

Abstract

Graph neural networks (GNNs) achieve strong performance on homophilic graphs but often struggle under heterophily, where adjacent nodes frequently belong to different classes. We propose an interpretable and adaptive framework for semi-supervised node classification based on explicit combinatorial inference rather than deep message passing. Our method assigns labels using a confidence-ordered greedy procedure driven by an additive scoring function that integrates class priors, neighborhood statistics, feature similarity, and training-derived label-label compatibility. A small set of transparent hyperparameters controls the relative influence of these components, enabling smooth adaptation between homophilic and heterophilic regimes. We further introduce a validation-gated hybrid strategy in which combinatorial predictions are optionally injected as priors into a lightweight neural model. Hybrid refinement is applied only when it improves validation performance, preserving interpretability when neuralization is unnecessary. All adaptation signals are computed strictly from training data, ensuring a leakage-free evaluation protocol. Experiments on heterophilic and transitional benchmarks demonstrate competitive performance with modern GNNs while offering advantages in interpretability, tunability, and computational efficiency.