Equivariant Subgraph Aggregation Networks

10/06/2021
by   Beatrice Bevilacqua, et al.
8

Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in their expressive power. This paper proposes a novel framework called Equivariant Subgraph Aggregation Networks (ESAN) to address this issue. Our main observation is that while two graphs may not be distinguishable by an MPNN, they often contain distinguishable subgraphs. Thus, we propose to represent each graph as a set of subgraphs derived by some predefined policy, and to process it using a suitable equivariant architecture. We develop novel variants of the 1-dimensional Weisfeiler-Leman (1-WL) test for graph isomorphism, and prove lower bounds on the expressiveness of ESAN in terms of these new WL variants. We further prove that our approach increases the expressive power of both MPNNs and more expressive architectures. Moreover, we provide theoretical results that describe how design choices such as the subgraph selection policy and equivariant neural architecture affect our architecture's expressive power. To deal with the increased computational cost, we propose a subgraph sampling scheme, which can be viewed as a stochastic version of our framework. A comprehensive set of experiments on real and synthetic datasets demonstrates that our framework improves the expressive power and overall performance of popular GNN architectures.

READ FULL TEXT
research
06/22/2022

Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries

Subgraph GNNs are a recent class of expressive Graph Neural Networks (GN...
research
04/14/2023

Combining Stochastic Explainers and Subgraph Neural Networks can Increase Expressivity and Interpretability

Subgraph-enhanced graph neural networks (SGNN) can increase the expressi...
research
06/22/2022

Ordered Subgraph Aggregation Networks

Numerous subgraph-enhanced graph neural networks (GNNs) have emerged rec...
research
05/31/2023

Improving Expressivity of Graph Neural Networks using Localization

In this paper, we propose localized versions of Weisfeiler-Leman (WL) al...
research
02/21/2022

1-WL Expressiveness Is (Almost) All You Need

It has been shown that a message passing neural networks (MPNNs), a popu...
research
11/21/2015

GradNets: Dynamic Interpolation Between Neural Architectures

In machine learning, there is a fundamental trade-off between ease of op...
research
06/06/2023

Fine-grained Expressivity of Graph Neural Networks

Numerous recent works have analyzed the expressive power of message-pass...

Please sign up or login with your details

Forgot password? Click here to reset