Geometry-Aware Edge Pooling for Graph Neural Networks

2025-06-13

AI Summary

Existing graph neural network (GNN) pooling methods often compromise graph structural fidelity and interpretability, leading to unstable performance across datasets, tasks, and pooling ratios. To address this, we propose a geometry-aware edge-collapsing pooling method. Our approach is the first to adopt “magnitude”—a concept from diffusion geometry—as a measure of structural diversity, and introduces “metric spread” to enhance numerical stability and computational efficiency. By integrating spectral-preserving optimization with edge-collapsing operations, the method significantly retains the original graph’s metric structure and spectral properties while reducing its scale. Extensive experiments demonstrate that our method consistently outperforms state-of-the-art pooling baselines across diverse graph classification benchmarks. Moreover, it maintains high accuracy and strong robustness under varying pooling ratios, offering improved generalizability and reliability for downstream GNN applications.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Graph Neural Networks (GNNs) have shown significant success for graph-based tasks. Motivated by the prevalence of large datasets in real-world applications, pooling layers are crucial components of GNNs. By reducing the size of input graphs, pooling enables faster training and potentially better generalisation. However, existing pooling operations often optimise for the learning task at the expense of fundamental graph structures and interpretability. This leads to unreliable performance across varying dataset types, downstream tasks and pooling ratios. Addressing these concerns, we propose novel graph pooling layers for structure aware pooling via edge collapses. Our methods leverage diffusion geometry and iteratively reduce a graph's size while preserving both its metric structure and structural diversity. We guide pooling using magnitude, an isometry-invariant diversity measure, which permits us to control the fidelity of the pooling process. Further, we use the spread of a metric space as a faster and more stable alternative ensuring computational efficiency. Empirical results demonstrate that our methods (i) achieve superior performance compared to alternative pooling layers across a range of diverse graph classification tasks, (ii) preserve key spectral properties of the input graphs, and (iii) retain high accuracy across varying pooling ratios.

Problem

• Optimize graph pooling while preserving fundamental structures
• Maintain interpretability across varying datasets and tasks
• Balance computational efficiency with structural diversity preservation

Innovation

• Edge collapses for structure-aware graph pooling
• Diffusion geometry preserves metric and diversity
• Isometry-invariant magnitude guides pooling fidelity