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

TL;DR

This paper introduces an interpretable, adaptive node classification framework for heterophilic graphs that combines combinatorial inference with hybrid learning, achieving competitive results while enhancing interpretability and efficiency.

Contribution

It presents a novel combinatorial scoring-based method with hybrid neural refinement for semi-supervised node classification on heterophilic graphs, emphasizing interpretability and adaptability.

Findings

Achieves competitive accuracy on heterophilic benchmarks

Offers a transparent, hyperparameter-controlled adaptation between regimes

Demonstrates improved interpretability and efficiency over traditional GNNs

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.