Fixed Aggregation Features Rival GNNs on 12 Benchmarks, Achieving State-Of-The-Art Results

Researchers are questioning the dominance of Graph Neural Networks (GNNs) in node representation learning, demonstrating that surprisingly simple, training-free methods can achieve comparable , and sometimes superior , results. Celia Rubio-Madrigal and Rebekka Burkholz, both from CISPA Helmholtz Center for Information Security, alongside et al., present Fixed Aggregation Features (FAFs), which recast graph learning as a tabular problem, allowing the application of established tabular methods. This innovative approach not only rivals state-of-the-art GNNs and transformers across twelve benchmark tasks, often utilising just mean aggregation, but also offers enhanced interpretability and deployment flexibility , challenging the necessity of complex, trainable neighbourhood aggregations and suggesting a need for more robust tabular baselines in graph learning evaluations.

The team achieved this breakthrough by leveraging the Kolmogorov, Arnold representation theorem, providing a lossless construction of neighborhood aggregations and theoretically enabling the encoding of neighbor features without information loss. However, the research exposed a crucial gap between expressiveness and learnability, noting that these lossless encoders are sensitive to numerical noise and produce Embeddings unsuitable for standard classifiers. Building on this, the scientists proposed FAFs, a training-free pipeline applying fixed aggregation functions over neighborhoods, concatenating the results into a tabular feature matrix, and then training a downstream classifier like an MLP.

This data transformation offers several advantages, including high interpretability through feature importance analysis and ablations, compatibility with the robust toolbox of tabular learning, architectural flexibility, and reduced computational demands. Empirically, FAFs combined with well-tuned MLP classifiers proved competitive on 12 out of 14 common node-classification benchmarks, encompassing citation, coauthor, Amazon co-purchase graphs, Wikipedia, and other heterophilous datasets. Performance only lagged on the Minesweeper and Roman Empire datasets, where the best GNNs utilise linear residual connections, the performance gap aligning with gains from parameterized residuals reported in prior work. Experiments show that these results suggest that many benchmarks do not necessitate sophisticated learned aggregations, and a substantial portion of GNN performance can be replicated by powerful tabular predictors fed with fixed, transparent features. The research establishes FAFs as both a strong baseline and a diagnostic tool for graph benchmarks and methods, offering a new perspective on optimization and enabling the identification of crucial signal-carrying hop distances and reducers. Experiments employed 14 benchmark datasets, including citation, co-author, and Amazon co-purchase graphs, to. The team measured performance across diverse graph structures, including citation, coauthor, and Amazon co-purchase graphs, consistently demonstrating competitive results with FAFs and MLPs. Notably, the best-performing FAF models utilized only 2, 4 hops, while the most effective GNNs on these benchmarks often employed 10, 15 layers, indicating a potential for increased efficiency. Data shows that FAFs, combined with well-tuned MLPs, achieved competitive results on 12 out of 14 common node-classification benchmarks, encompassing datasets like those from Wikipedia and various heterophilous sources.
The breakthrough delivers a decoupling of representation from optimization, allowing standard interpretability tools to identify signal-carrying hop distances and reducers within the graph structure. Measurements confirm that for most benchmarks, the relevant signal is concentrated within the first two hops, with sum and mean aggregation preserving crucial information. Tests prove that while different reducers become complementary at higher hops, the information gain from min/max diminishes, highlighting the importance of carefully selecting aggregation functions. This work connects findings to the Kolmogorov, Arnold representation theorem, providing a theoretical basis for the possibility of non-trainable aggregations and demonstrating when mean aggregation can be sufficient for effective performance. The authors acknowledge limitations in the practical application of Kolmogorov-Arnold representations, noting occasional training instability and mild overfitting, and suggest that future work should focus on developing benchmarks that genuinely demand long-range dependencies and inter-hop dynamics. They also advocate for simplifying models and prioritising optimisability alongside expressiveness, as some limitations may originate from dataset characteristics rather than graph architectures themselves.