Curvature-based Pooling within Graph Neural Networks

TL;DR

This paper introduces CurvPool, a novel graph pooling method that uses graph curvature to improve information propagation in GNNs, addressing over-squashing and over-smoothing issues for better graph classification.

Contribution

CurvPool leverages graph curvature to adaptively cluster nodes, enabling deeper GNNs and more effective long-distance information propagation, outperforming existing pooling methods.

Findings

CurvPool improves classification accuracy over state-of-the-art methods.

It effectively mitigates over-smoothing and over-squashing.

Densely connected cluster pooling with sum aggregation yields best results.

Abstract

Over-squashing and over-smoothing are two critical issues, that limit the capabilities of graph neural networks (GNNs). While over-smoothing eliminates the differences between nodes making them indistinguishable, over-squashing refers to the inability of GNNs to propagate information over long distances, as exponentially many node states are squashed into fixed-size representations. Both phenomena share similar causes, as both are largely induced by the graph topology. To mitigate these problems in graph classification tasks, we propose CurvPool, a novel pooling method. CurvPool exploits the notion of curvature of a graph to adaptively identify structures responsible for both over-smoothing and over-squashing. By clustering nodes based on the Balanced Forman curvature, CurvPool constructs a graph with a more suitable structure, allowing deeper models and the combination of distant information. We compare it to other state-of-the-art pooling approaches and establish its competitiveness in terms of classification accuracy, computational complexity, and flexibility. CurvPool outperforms several comparable methods across all considered tasks. The most consistent results are achieved by pooling densely connected clusters using the sum aggregation, as this allows additional information about the size of each pool.