Invariant-Stratified Propagation for Expressive Graph Neural Networks

2026-03-01

AI Summary

This work addresses the limited expressivity of graph neural networks (GNNs), which are constrained by the 1-Weisfeiler-Lehman (1-WL) test and thus unable to distinguish graph structures beyond degree sequences or capture nodes’ structural roles in higher-order interactions. To overcome this, we propose the ISP-WL test and its neural instantiation, ISPGNN, which for the first time integrates a hierarchy based on graph invariants into message passing. By hierarchically encoding structural heterogeneity, ISPGNN explicitly models nodes’ higher-order roles across multiple levels, thereby surpassing the expressiveness of 1-WL. The method exhibits strong resistance to oversmoothing and flexible structure-aware capabilities, achieving significant performance gains over existing GNNs and high-expressivity models on graph classification, node classification, and influence estimation tasks, demonstrating its effectiveness and generalization ability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Graphical Models

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks (GNNs) face fundamental limitations in expressivity and capturing structural heterogeneity. Standard message-passing architectures are constrained by the 1-dimensional Weisfeiler-Leman (1-WL) test, unable to distinguish graphs beyond degree sequences, and aggregate information uniformly from neighbors, failing to capture how nodes occupy different structural positions within higher-order patterns. While methods exist to achieve higher expressivity, they incur prohibitive computational costs and lack unified frameworks for flexibly encoding diverse structural properties. To address these limitations, we introduce Invariant-Stratified Propagation (ISP), a framework comprising both a novel WL variant (ISP-WL) and its efficient neural network implementation (ISPGNN). ISP stratifies nodes according to graph invariants, processing them in hierarchical strata that reveal structural distinctions invisible to 1-WL. Through hierarchical structural heterogeneity encoding, ISP quantifies differences in nodes' structural positions within higher-order patterns, distinguishing interactions where participants occupy different roles from those with uniform participation. We provide formal theoretical analysis establishing enhanced expressivity beyond 1-WL, convergence guarantees, and inherent resistance to oversmoothing. Extensive experiments across graph classification, node classification, and influence estimation demonstrate consistent improvements over standard architectures and state-of-the-art expressive baselines.

Problem

• Graph Neural Networks
• expressivity
• structural heterogeneity
• Weisfeiler-Leman test
• message-passing

Innovation

• Invariant-Stratified Propagation
• Graph Neural Networks
• Weisfeiler-Leman test
• Structural Heterogeneity
• Expressivity