Weisfeiler and Leman Go Measurement Modeling: Probing the Validity of the WL Test

TL;DR

This paper critically examines the limitations of the $k$-WL test in measuring the expressive power of graph neural networks, revealing misalignments with practitioners' beliefs and proposing benchmark-based evaluation methods.

Contribution

It uncovers the misalignments between $k$-WL and practical understanding of expressive power, and proposes benchmark-based measurement and guiding questions for better evaluation.

Findings

$k$-WL does not guarantee isometry.

$k$-WL can be irrelevant to real-world tasks.

$k$-WL may not promote generalization or trustworthiness.

Abstract

The expressive power of graph neural networks is usually measured by comparing how many pairs of graphs or nodes an architecture can possibly distinguish as non-isomorphic to those distinguishable by the $k$-dimensional Weisfeiler-Leman ($k$-WL) test. In this paper, we uncover misalignments between graph machine learning practitioners' conceptualizations of expressive power and $k$-WL through a systematic analysis of the reliability and validity of $k$-WL. We conduct a survey ($n = 18$) of practitioners to surface their conceptualizations of expressive power and their assumptions about $k$-WL. In contrast to practitioners' beliefs, our analysis (which draws from graph theory and benchmark auditing) reveals that $k$-WL does not guarantee isometry, can be irrelevant to real-world graph tasks, and may not promote generalization or trustworthiness. We argue for extensional definitions and measurement of expressive power based on benchmarks. We further contribute guiding questions for constructing such benchmarks, which is critical for graph machine learning practitioners to develop and transparently communicate our understandings of expressive power.