Preben M. Ness, Fariz Ikhwantri, Dusica Marijancs.LG
Are heterophilic nodes in a graph harder to classify because they are heterophilic or because they are rare? Some existing work frames classification of such nodes as a subgroup generalisation problem, where a model performs well on the majority group at the expense of the rare group. Others explain this as a problem of neighbourhood aggregation in graph neural networks (GNNs). We assess these two viewpoints through a detailed evaluation of six GNNs on five datasets of varying homophily, and find that homophilic nodes tend to be easier to classify, even when they are rare---challenging the subgroup framing. However, our findings also nuance existing beliefs about how GNNs misrepresent heterophilic nodes. We demonstrate that the information needed to classify heterophilic nodes correctly is often recoverable by retraining the classification head of a model, or even just the final linear classification layer.
Graph attention normalizes neighborhood scores with softmax, the maximum-entropy choice under Shannon statistics. But homophilic and heterophilic graphs want different attention shapes, and one fixed normalization cannot serve both. We propose \textbf{LTGA} (\textbf{L}earnable \textbf{T}sallis \textbf{G}raph \textbf{A}ttention), a graph attention layer whose Tsallis entropic index $q$ is learned jointly with the weights, interpolating continuously between heavy-tailed ($q\!<\!1$), softmax ($q\!=\!1$) and compact-support ($q\!>\!1$) attention at four granularities from a global scalar to a per-edge index, under a bounded reparameterization that starts every model at the GAT baseline. Across eight benchmarks at ten seeds, LTGA-Edge takes the best average rank ($2.75$), but the omnibus test does not reject ($p\!=\!0.199$) and learning $q$ does not beat searching it: a validation-tuned frozen grid reaches $61.4\%$, tuned $α$-entmax $62.2\%$ and a capacity-matched $q\!\equiv\!1$ control $62.0\%$, against $61.7\%$ for LTGA-Edge. What the learned index buys is one run instead of a grid, and an interpretable mechanism: where $q$ leaves $1$, it prunes $42\%$ of attention coefficients to exactly zero, and those edges are selectively the wrong ones, restoring them costs $7.1$ points, while random pruning at the same rate costs $13.0$ more. Project page: https://kleyt0n.github.io/ltga
Conformal prediction (CP) provides distribution-free uncertainty quantification, and its extension to graphs is an active research direction. Diffused Adaptive Prediction Sets (DAPS) is a widely used graph-aware diffusion baseline, propagating Adaptive Prediction Sets (APS) non-conformity scores along edges with a uniform coefficient $λ$. We identify a fundamental shortcoming of this design: the uniform low-pass diffusion presupposes graph homophily and proves detrimental on heterophilic graphs, enlarging the mean prediction-set size by up to 10.6% relative to plain APS. To mitigate this, we propose HeAD-CP, a family of node-wise diffusion variants whose coefficients are determined by a label-free local-homophily estimate derived from the GNN softmax. Three variants, namely signed-$γ$, edge-compatibility, and a DAPS-baseline-with-correction, are most effective at extreme heterophily, intermediate heterophily, and moderate-to-high homophily, respectively, and all preserve the marginal coverage guarantee. On ten benchmarks, the HeAD-CP family stays at or below plain APS on every dataset, while DAPS exceeds APS on six. The post-hoc oracle over the family improves over DAPS on 8/10 datasets at $p<0.01$ (paired Wilcoxon), with the largest gains on heterophilic graphs (10.3% on Texas); on the two homophilic datasets where DAPS still wins (CiteSeer, PubMed), it retains a marginal advantage of at most 0.002, statistically insignificant on CiteSeer ($p=0.23$). Designing a calibrated label-free selector that approaches this oracle is the main outstanding empirical question.
Guoming Li, Jian Yang, Xukun Wang +3cs.LG eess.SP math.NA
Coarsening-based training for graph neural networks (GNNs), i.e.\ training on coarsened graphs rather than the original large ones, has become a promising direction for scaling GNNs to massive graphs. However, prior work has been evaluated almost exclusively on \textit{homophilic} graphs, leaving the more challenging \textit{heterophilic} settings underexplored. We show, both empirically and theoretically, that existing coarsening-based training methods suffer significant performance degradation on heterophilic graphs due to inevitable loss of graph information during coarsening. To address this, we propose {\bf A}daptive {\bf C}omplementary {\bf E}nhancement, a plug-and-play, model-agnostic strategy that reintegrates the information discarded in coarsening: ACE learns a projector for re-constructing original node features and applies \textit{anisotropic structural regularization} to embed local heterophily. We further adopt \textit{homoscedastic uncertainty weighting} to adaptively balance the combined training objective of primary coarsened-graph training loss and full-graph auxiliary loss with augmented node features re-constructed by the heterophily-aware projector. Extensive experiments show that ACE drives consistent gains on heterophilic benchmarks while preserving competitive results on homophilic graphs with minimal computational overhead. Code is available at the GitHub repository: https://github.com/vasile-paskardlgm/ACE.
We introduce a constrained two-view framework for node prediction that aligns structure-conditioned GNN embeddings with a structure-free feature prior learned by an anchor model. Conventional Graph Neural Networks (GNNs) couple feature transformation and neighborhood aggregation, which renders them vulnerable to topology noise and heterophilous connections. To decouple this dependency, our framework utilizes an independent anchor network to capture intrinsic attribute features via a self-supervised reconstruction objective. Furthermore, we propose a Channel-Split Adaptive Gated GNN (CSAG-GNN) that dynamically routes representations between global spectral smoothing and local spatial discrimination through a node-wise gating mechanism. We propose a stable cyclic alternating optimization strategy to solve the resulting coupled bi-level objective, preventing mutual representation drift during training. Empirical results on both homophilous and heterophilous benchmarks show balanced performance gains and structural robustness over competitive baselines.
Federated Graph Learning facilitates collaborative graph modeling across distributed clients while preserving data privacy. However, real-world data categories frequently exhibit long-tailed distributions. Such statistical scarcity severely degrades performance in two ways: it biases the global model toward majority classes, and it structurally isolates minority nodes by submerging them in heterophilic, head-dominated neighborhoods. While existing methods attempt topology-agnostic statistical compensations, they often fail under data scarcity. Instead of recovering tail nodes, they overfit the structural noise from adjacent dominant classes, leading to representation degradation. To address these limitations, we propose FedEPD, a framework built on a dual decoupling paradigm that separates topological purification from semantic recalibration. Specifically, FedEPD utilizes distribution-aware Dirichlet energy pruning to filter spatial heterophilic edges. It then overcomes Non-IID distribution shifts by extracting robust global prototypes from topologically central nodes, which are incorporated into local representations via a spatial low-pass prototype injection. Furthermore, a two stage alternating optimization strategy strictly protects majority decision boundaries while improving minority accuracy. Extensive experiments demonstrate that FedEPD achieves state-of-the-art performance across diverse long-tailed benchmarks, yielding absolute improvements of up to 4.97% in Accuracy and 5.48% in Macro-F1.
Hypergraph knowledge distillation aims to retain the predictive performance of a hypergraph neural network (HNN) teacher while reducing inference costs through a lightweight student model. In this work, we observe that HNNs exhibit substantially lower prediction performance on heterophilic nodes connected through semantically diverse hyperedges, indicating that the reliability of teacher knowledge varies across nodes. Motivated by this observation, we propose HADES, a heterophily-aware adaptive distillation method for hypergraph neural networks. HADES quantifies node heterophily and leverages it as an estimate of teacher reliability to modulate the transfer of teacher knowledge during distillation. Experimental results on real-world hypergraphs demonstrate that HADES consistently improves student performance across different HNN teachers and distillation objectives. In many cases, the resulting student models surpass the predictive performance of their teachers while achieving up to 12.3 times faster inference.
Many real-world heterogeneous graphs exhibit pronounced heterophily, where connected nodes often have dissimilar labels or play different semantic roles. In such settings, standard heterogeneous graph neural networks that aggregate messages along metapaths or meta-relations primarily based on feature similarity can propagate misleading information, since feature similarity may be misaligned with underlying relational semantics. In this paper, we propose HeterSEED, a semantics-structure decoupling framework for heterogeneous graph learning under heterophily. HeterSEED decouples representation learning into a heterogeneous semantic channel that captures type- and relation-aware local semantics and a structure-aware heterophily channel that separates homophilic and heterophilic neighborhoods via pseudo-label-guided partitioning and aggregates them using metapath-based structural weights. A node-level adaptive fusion mechanism then combines the two channels to produce context-dependent node representations. Theoretically, we establish that, on heterogeneous graphs under heterophily, HeterSEED is strictly more expressive than standard heterogeneous graph neural networks that rely primarily on feature similarity and provably reduces the prediction bias introduced by heterophilic neighbors. Experiments on five real-world heterogeneous graphs, including two large-scale networks at the million-node and hundred-million-edge scale, demonstrate that HeterSEED consistently outperforms representative heterogeneous graph neural networks and recent heterophily-aware baselines, especially in strongly heterophilic regimes.
Heterogeneous graphs with heterophily have emerged as a powerful abstraction for modeling complex real-world systems, where nodes of different types and labels interact in diverse and often non-homophilous ways. Despite recent advances, robust representation learning for such graphs remains largely unexplored, particularly in the presence of noisy or misleading connectivity. In this work, we investigate this problem and identify structural noise as a critical challenge that significantly degrades model performance. To address this issue, we propose a unified framework, Heterogeneous Graph Unified Learning (HGUL), which jointly handles heterophily and noisy graph structures. The framework consists of three complementary modules: a kNN-based graph construction module that recovers reliable local neighborhoods, a graph structure learning module that adaptively refines the adjacency by filtering noisy edges, and a heterogeneous affinity learning module that captures class-level relationships via an extended affinity matrix derived from a polynomial graph kernel. Extensive experiments on multiple datasets demonstrate that HGUL consistently outperforms existing methods on clean graphs and maintains strong robustness under varying levels of structural noise. The results further underscore the importance of jointly modeling heterophily and noise in heterogeneous graph learning.