The Role of Node Features in Graph Pooling

TL;DR

This paper investigates how the quality and alignment of node features with graph topology influence the effectiveness of graph pooling in classification tasks.

Contribution

It formalizes the conditions for node features to enable effective pooling and introduces a measure of feature quality, highlighting their importance.

Findings

Properly aligned node features improve pooling performance.

Pooling benefits are dataset-dependent and require specific feature conditions.

A new quantitative measure assesses feature quality for pooling effectiveness.

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.