Graph Neural Networks Are More Powerful Than we Think

05/19/2022
by   Charilaos I. Kanatsoulis, et al.
0

Graph Neural Networks (GNNs) are powerful convolutional architectures that have shown remarkable performance in various node-level and graph-level tasks. Despite their success, the common belief is that the expressive power of GNNs is limited and that they are at most as discriminative as the Weisfeiler-Lehman (WL) algorithm. In this paper we argue the opposite and show that the WL algorithm is the upper bound only when the input to the GNN is the vector of all ones. In this direction, we derive an alternative analysis that employs linear algebraic tools and characterize the representational power of GNNs with respect to the eigenvalue decomposition of the graph operators. We show that GNNs can distinguish between any graphs that differ in at least one eigenvalue and design simple GNN architectures that are provably more expressive than the WL algorithm. Thorough experimental analysis on graph isomorphism and graph classification datasets corroborates our theoretical results and demonstrates the effectiveness of the proposed architectures.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/01/2018

How Powerful are Graph Neural Networks?

Graph Neural Networks (GNNs) for representation learning of graphs broad...
research
10/01/2021

Reconstruction for Powerful Graph Representations

Graph neural networks (GNNs) have limited expressive power, failing to r...
research
01/23/2023

Rethinking the Expressive Power of GNNs via Graph Biconnectivity

Designing expressive Graph Neural Networks (GNNs) is a central topic in ...
research
06/28/2020

Characterizing the Expressive Power of Invariant and Equivariant Graph Neural Networks

Various classes of Graph Neural Networks (GNN) have been proposed and sh...
research
02/22/2023

Equivariant Polynomials for Graph Neural Networks

Graph Neural Networks (GNN) are inherently limited in their expressive p...
research
01/26/2023

WL meet VC

Recently, many works studied the expressive power of graph neural networ...
research
11/14/2018

Pitfalls of Graph Neural Network Evaluation

Semi-supervised node classification in graphs is a fundamental problem i...

Please sign up or login with your details

Forgot password? Click here to reset