Graph Neural Networks Are More Powerful Than we Think

Charilaos Kanatsoulis, Alejandro Ribeiro

Keywords: graph neural networks, expressive power, representation, graph isomorphism, classification, spectral decomposition

Abstract: 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 standard 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.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Deep Learning and representational learning

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/graph-neural-networks-are-more-powerful-than/code)