Expressive Power of Temporal Message Passing

TL;DR

This paper analyzes the expressive power of temporal message-passing mechanisms in graph neural networks, establishing formal characterizations and comparing their capabilities on different types of temporal graphs.

Contribution

It introduces Weisfeiler-Leman characterizations for global and local temporal message passing, revealing their incomparability and relative expressiveness on specific graph classes.

Findings

Global and local mechanisms have incomparable expressive power.

Local mechanism is more expressive on colour-persistent graphs.

Experimental results support theoretical analysis.

Abstract

Graph neural networks (GNNs) have recently been adapted to temporal settings, often employing temporal versions of the message-passing mechanism known from GNNs. We divide temporal message passing mechanisms from literature into two main types: global and local, and establish Weisfeiler-Leman characterisations for both. This allows us to formally analyse expressive power of temporal message-passing models. We show that global and local temporal message-passing mechanisms have incomparable expressive power when applied to arbitrary temporal graphs. However, the local mechanism is strictly more expressive than the global mechanism when applied to colour-persistent temporal graphs, whose node colours are initially the same in all time points. Our theoretical findings are supported by experimental evidence, underlining practical implications of our analysis.