The Role of Node Features in Graph Pooling

2026-05-07

AI Summary

Graph pooling often struggles to consistently surpass the expressive power of 1-WL-equivalent GNNs in graph classification tasks, yielding limited performance gains. This work identifies that effective pooling hinges on the alignment between node features and graph topology, and for the first time formally defines the fundamental conditions that node features must satisfy to enable such effective pooling. Building on this insight, we introduce a quantitative metric to measure the degree of feature–topology alignment. Both theoretical analysis and empirical experiments demonstrate that when node features meet the proposed conditions, graph pooling can significantly enhance classification performance on suitable datasets.

Abstract

Graph pooling is commonly applied in graph classification, yet its empirical gains over standard WL-1 expressive GNNs are often marginal or inconsistent. We study this gap by analysing the interaction between node features and graph topology and their effect on pooling objectives. Our analysis reveals that pooling operators require node features that are well-aligned with the graph's topology -- a condition often overlooked and not guaranteed in empirical networks. We formalise fundamental requirements for node features to enable effective pooling, and introduce a quantitative measure of feature quality. Our empirical evaluation shows that, when these requirements are satisfied, pooling can be beneficial and improve performance on appropriate datasets.

Problem

• graph pooling
• node features
• graph topology
• graph classification
• feature alignment

Innovation

• graph pooling
• node features
• topology alignment
• feature quality
• GNN expressiveness