1-WL Expressiveness Is (Almost) All You Need

TL;DR

This paper demonstrates that the expressive power of 1-WL-based neural networks is sufficient for most graph classification tasks, with their practical performance nearly reaching theoretical limits in standard datasets.

Contribution

The study shows that the limited expressiveness of 1-WL is not a practical bottleneck for graph neural networks in common datasets, challenging the need for more complex models.

Findings

1-WL suffices to identify almost all graphs in standard datasets.

Classification accuracy upper bounds are close to 100%.

Simple WL-based neural networks perform well across datasets.

Abstract

It has been shown that a message passing neural networks (MPNNs), a popular family of neural networks for graph-structured data, are at most as expressive as the first-order Weisfeiler-Leman (1-WL) graph isomorphism test, which has motivated the development of more expressive architectures. In this work, we analyze if the limited expressiveness is actually a limiting factor for MPNNs and other WL-based models in standard graph datasets. Interestingly, we find that the expressiveness of WL is sufficient to identify almost all graphs in most datasets. Moreover, we find that the classification accuracy upper bounds are often close to 100\%. Furthermore, we find that simple WL-based neural networks and several MPNNs can be fitted to several datasets. In sum, we conclude that the performance of WL/MPNNs is not limited by their expressiveness in practice.