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

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.

Minimum Weighted Feedback Arc Sets for Ranking from Pairwise Comparisons

The Minimum Weighted Feedback Arc Set (MWFAS) problem is fundamentally connected to the Ranking Problem -- the task of deriving global rankings from pairwise comparisons. Recent work [He et al. ICML2022] has advanced the state-of-the-art for the Ranking Problem using learning-based methods, improving upon multiple previous approaches. However, the connection to MWFAS remains underexplored. This paper investigates this relationship and presents efficient combinatorial algorithms for solving MWFAS, thus addressing the Ranking Problem. Our experimental results demonstrate that these simple, learning-free algorithms not only significantly outperform learning-based methods in terms of speed but also generally achieve superior ranking accuracy.