Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries

TL;DR

This paper analyzes the symmetry properties of Subgraph GNNs, establishes their expressive power limit at 3-WL, and introduces a new architecture, SUN, that unifies and improves upon previous models.

Contribution

It provides a symmetry analysis of node-based Subgraph GNNs, links them to Invariant Graph Networks, and proposes a novel, more powerful Subgraph GNN architecture called SUN.

Findings

SUN outperforms previous models on multiple benchmarks.

Subgraph GNNs are bounded by 3-WL in expressive power.

A novel symmetry analysis reduces the symmetry group needed for modeling subgraph collections.

Abstract

Subgraph GNNs are a recent class of expressive Graph Neural Networks (GNNs) which model graphs as collections of subgraphs. So far, the design space of possible Subgraph GNN architectures as well as their basic theoretical properties are still largely unexplored. In this paper, we study the most prominent form of subgraph methods, which employs node-based subgraph selection policies such as ego-networks or node marking and deletion. We address two central questions: (1) What is the upper-bound of the expressive power of these methods? and (2) What is the family of equivariant message passing layers on these sets of subgraphs?. Our first step in answering these questions is a novel symmetry analysis which shows that modelling the symmetries of node-based subgraph collections requires a significantly smaller symmetry group than the one adopted in previous works. This analysis is then used to establish a link between Subgraph GNNs and Invariant Graph Networks (IGNs). We answer the questions above by first bounding the expressive power of subgraph methods by 3-WL, and then proposing a general family of message-passing layers for subgraph methods that generalises all previous node-based Subgraph GNNs. Finally, we design a novel Subgraph GNN dubbed SUN, which theoretically unifies previous architectures while providing better empirical performance on multiple benchmarks.