FlowPool: Pooling Graph Representations with Wasserstein Gradient Flows

TL;DR

FlowPool introduces a graph pooling method that uses Wasserstein gradient flows to optimally preserve graph statistics, improving graph classification performance while maintaining permutation invariance.

Contribution

The paper proposes FlowPool, a novel Wasserstein gradient flow-based pooling method that preserves graph representation statistics and is compatible with end-to-end deep learning architectures.

Findings

FlowPool outperforms existing pooling methods in graph classification tasks.

The method is permutation invariant and adaptable to various representation geometries.

Experimental results show improved accuracy on benchmark datasets.

Abstract

In several machine learning tasks for graph structured data, the graphs under consideration may be composed of a varying number of nodes. Therefore, it is necessary to design pooling methods that aggregate the graph representations of varying size to representations of fixed size which can be used in downstream tasks, such as graph classification. Existing graph pooling methods offer no guarantee with regards to the similarity of a graph representation and its pooled version. In this work, we address this limitation by proposing FlowPool, a pooling method that optimally preserves the statistics of a graph representation to its pooled counterpart by minimising their Wasserstein distance. This is achieved by performing a Wasserstein gradient flow with respect to the pooled graph representation. Our method relies on a versatile implementation which can take into account the geometry of the representation space through any ground cost and computes the gradient of the Wasserstein distance with automatic differentiation. We propose the differentiation of the Wasserstein flow layer using an implicit differentiation scheme. Therefore, our pooling method is amenable to automatic differentiation and can be integrated in end-to-end deep learning architectures. Further, FlowPool is invariant to permutations and can therefore be combined with permutation equivariant feature extraction layers in GNNs in order to obtain predictions that are independent of the ordering of the nodes. Experimental results demonstrate that our method leads to an increase in performance compared to existing pooling methods when evaluated on graph classification.