Subgraph Permutation Equivariant Networks

TL;DR

Subgraph Permutation Equivariant Networks (SPEN) introduce a scalable, local approach to permutation-equivariant graph neural networks that enhances expressive power and reduces memory usage, validated on multiple benchmarks.

Contribution

The paper presents a novel framework for subgraph-based permutation equivariant networks that improves scalability and expressive power over existing global methods.

Findings

Achieves state-of-the-art results on six out of seven graph classification benchmarks.

Offers significant GPU memory savings compared to global permutation equivariant methods.

Demonstrates flexibility with different sub-graph sizes and representation spaces.

Abstract

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of $k$-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.