Neighbourhood Transformer: Switchable Attention for Monophily-Aware Graph Learning

Heterophily is a prevalent property of real-world graphs and is well known to impair the performance of homophilic Graph Neural Networks (GNNs). Prior work has attempted to adapt GNNs to heterophilic graphs through non-local neighbor extension or architecture refinement. However, the fundamental reasons behind misclassifications remain poorly understood. In this work, we take a novel perspective by examining recurring inductive subgraphs, empirically and theoretically showing that they act as spurious shortcuts that mislead GNNs and reinforce non-causal correlations in heterophilic graphs. To address this, we adopt a causal inference perspective to analyze and correct the biased learning behavior induced by shortcut inductive subgraphs. We propose a debiased causal graph that explicitly blocks confounding and spillover paths responsible for these shortcuts. Guided by this causal graph, we introduce Causal Disentangled GNN (CD-GNN), a principled framework that disentangles spurious inductive subgraphs from true causal subgraphs by explicitly blocking non-causal paths. By focusing on genuine causal signals, CD-GNN substantially improves the robustness and accuracy of node classification in heterophilic graphs. Extensive experiments on real-world datasets not only validate our theoretical findings but also demonstrate that our proposed CD-GNN outperforms state-of-the-art heterophily-aware baselines.

Over the past decade, Graph Neural Networks (GNNs) have achieved great success on machine learning tasks with relational data. However, recent studies have found that heterophily can cause significant performance degradation of GNNs, especially on node-level tasks. Numerous heterophilic benchmark datasets have been put forward to validate the efficacy of heterophily-specific GNNs, and various homophily metrics have been designed to help recognize these challenging datasets. Nevertheless, there still exist multiple pitfalls that severely hinder the proper evaluation of new models and metrics: 1) lack of hyperparameter tuning; 2) insufficient evaluation on the truly challenging heterophilic datasets; 3) missing quantitative evaluation for homophily metrics on synthetic graphs. To overcome these challenges, we first train and fine-tune baseline models on $27$ most widely used benchmark datasets, and categorize them into three distinct groups: malignant, benign and ambiguous heterophilic datasets. We identify malignant and ambiguous heterophily as the truly challenging subsets of tasks, and to our best knowledge, we are the first to propose such taxonomy. Then, we re-evaluate $11$ state-of-the-arts (SOTA) GNNs, covering six popular methods, with fine-tuned hyperparameters on different groups of heterophilic datasets. Based on the model performance, we comprehensively reassess the effectiveness of different methods on heterophily. At last, we evaluate $11$ popular homophily metrics on synthetic graphs with three different graph generation approaches. To overcome the unreliability of observation-based comparison and evaluation, we conduct the first quantitative evaluation and provide detailed analysis.

Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for heterophilous graph classification suffer from hub-dominated (node with large degree) aggregation and oversmoothing, as their suboptimal polynomial filters introduce approximation errors and blend distant signals. To address the degree-biased aggregation and suboptimal polynomial filtering, we introduce a Hierarchical Multi-view HAAR (HMH), a novel spectral graph-learning framework that scales in near-linear time . HMH first learns feature- and structure-aware signed affinities via a heterophily-aware encoder, then constructs a soft graph hierarchy guided by these embeddings. At each hierarchical level, HMH constructs a sparse, orthonormal, and locality-aware Haar basis to apply learnable spectral filters in the frequency domain. Finally, skip-connection unpooling layers combine outputs from all hierarchical levels back into the original graph, effectively preventing hub domination and long-range signal bottleneck (over-squashing). Experimentation shows that HMH outperforms state-of-the-art spectral baselines, achieving up to a 3% improvement on node classification and 7% points on graph classification datasets, all while maintaining linear scalability.