Unifying approach to uniform expressivity of graph neural networks

2026-02-20

AI Summary

Existing graph neural networks (GNNs) struggle to effectively capture substructural information in graphs, limiting their expressive power. This work proposes Template Graph Neural Networks (T-GNNs), a novel framework that enhances node representations by aggregating embeddings from a predefined set of graph templates, and formally establishes the first general architecture for substructure-augmented GNNs. The core contribution lies in proving the equivalence between T-GNNs and graded modal logic with templates, denoted GML(T), and in introducing template bisimulation and a template-based Weisfeiler–Leman algorithm, which together provide a unified theoretical lens for analyzing GNN expressiveness. The framework subsumes AC-GNNs and their recent variants as special cases, thereby demonstrating its generality and effectiveness.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

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
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

The expressive power of Graph Neural Networks (GNNs) is often analysed via correspondence to the Weisfeiler-Leman (WL) algorithm and fragments of first-order logic. Standard GNNs are limited to performing aggregation over immediate neighbourhoods or over global read-outs. To increase their expressivity, recent attempts have been made to incorporate substructural information (e.g. cycle counts and subgraph properties). In this paper, we formalize this architectural trend by introducing Template GNNs (T-GNNs), a generalized framework where node features are updated by aggregating over valid template embeddings from a specified set of graph templates. We propose a corresponding logic, Graded template modal logic (GML(T)), and generalized notions of template-based bisimulation and WL algorithm. We establish an equivalence between the expressive power of T-GNNs and GML(T), and provide a unifying approach for analysing GNN expressivity: we show how standard AC-GNNs and its recent variants can be interpreted as instantiations of T-GNNs.

Problem

• Graph Neural Networks
• expressive power
• substructure
• Weisfeiler-Leman algorithm
• first-order logic

Innovation

• Template GNNs
• expressive power
• graded template modal logic
• graph templates
• Weisfeiler-Leman algorithm