The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learning

Evaluating Knowledge Graph Completion (KGC) models remains challenging because standard assessment relies on isolated rank-based metrics such as MRR, Hits$@$k, and Mean Rank, which often produce conflicting model orderings across datasets. A model that leads on MRR may trail on Hits@1, and strong performance on one dataset may not generalize to another. This fragmentation hinders comparison, enables selective reporting, and obscures real progress. We reframe KGC evaluation as a Multi-Criteria Decision-Making (MCDM) problem and present a meta-analysis of seven aggregators across five tests: consistency, cross-dataset stability, metric independence, robustness under noise, and generalizability. Each test is averaged over leave-one-model-out (LOMO) and leave-one-group-out (LOGO) removals so that reliability reflects aggregator behavior across diverse model subsets. Across tail $(h,r,?)$ and relation $(h,?,t)$ prediction, Pareto-optimal analysis identifies Z-score as the most balanced aggregator, which ranks DualE highest for tail prediction and FMS (Flow-Modulated Scoring) highest for relation prediction. A test-sensitivity analysis using the same removals shows that consistency and stability are largely removal-invariant, while generalizability and independence are the most sensitive. The framework resolves evaluation inconsistencies and offers evidence-based guidance for aggregator selection and model benchmarking in KGC.

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.

Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated by the fact that topological objects permit operations, such as structural refinements, that are not appropriate for graph data. In this work, we extend MANTRA, a benchmark dataset containing manifold triangulations, to a larger class of manifolds with more diverse homeomorphism types. We show that, unlike prior claims, both graph neural networks (GNNs) and higher-order message passing (HOMP) methods can saturate the benchmark. However, we find that this is contingent on the right representation and feature assignment, emphasizing their importance in baseline models. We thus provide a novel evaluation protocol based on representational diversity and triangulation refinement. Surprisingly, we find no indication that existing models are capable of generalizing beyond the combinatorial structure of the data. This points towards a research gap in developing models that understand topological structure independent of scale. Our work thus provides the necessary scaffolding to evaluate future models and enable the development of topology-aware inductive biases.