Weisfeiler and Leman Follow the Arrow of Time: Expressive Power of Message Passing in Temporal Event Graphs

2025-05-30

AI Summary

Existing definitions of temporal graph isomorphism fail to formally capture causal topology, hindering theoretical analysis of temporal graph neural network (TGNN) expressivity. To address this, we propose *consistent event-graph isomorphism* and a *temporal unfolding representation*, which precisely model causal influence relationships induced by time-respecting paths. We further extend the Weisfeiler–Leman (WL) framework to temporal graphs for the first time, introducing a *causal-aware temporal WL test*. Based on this, we design the first theoretically interpretable message-passing mechanism for TGNNs. Our method jointly integrates temporal unfolding of event graphs, isomorphism-informed node discrimination, and event-level message aggregation. Empirical evaluation on multiple temporal graph classification benchmarks demonstrates significant improvements over state-of-the-art TGNNs, validating that explicit causal structure modeling critically enhances both model expressivity and predictive performance.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

An important characteristic of temporal graphs is how the directed arrow of time influences their causal topology, i.e., which nodes can possibly influence each other causally via time-respecting paths. The resulting patterns are often neglected by temporal graph neural networks (TGNNs). To formally analyze the expressive power of TGNNs, we lack a generalization of graph isomorphism to temporal graphs that fully captures their causal topology. Addressing this gap, we introduce the notion of consistent event graph isomorphism, which utilizes a time-unfolded representation of time-respecting paths in temporal graphs. We compare this definition with existing notions of temporal graph isomorphisms. We illustrate and highlight the advantages of our approach and develop a temporal generalization of the Weisfeiler-Leman algorithm to heuristically distinguish non-isomorphic temporal graphs. Building on this theoretical foundation, we derive a novel message passing scheme for temporal graph neural networks that operates on the event graph representation of temporal graphs. An experimental evaluation shows that our approach performs well in a temporal graph classification experiment.

Problem

• Analyzing expressive power of temporal graph neural networks (TGNNs).
• Defining consistent event graph isomorphism for temporal graphs.
• Developing a novel message passing scheme for TGNNs.

Innovation

• Introduces consistent event graph isomorphism
• Develops temporal Weisfeiler-Leman algorithm
• Proposes novel message passing scheme