Invariant-Stratified Propagation for Expressive Graph Neural Networks

TL;DR

This paper introduces Invariant-Stratified Propagation (ISP), a novel framework that enhances the expressivity of Graph Neural Networks by hierarchically encoding structural heterogeneity, surpassing the limitations of traditional message-passing methods.

Contribution

The authors propose ISP, including a new Weisfeiler-Leman variant and neural implementation, to better capture structural roles and higher-order patterns in graphs with theoretical guarantees.

Findings

ISP outperforms standard GNNs and state-of-the-art baselines in various graph tasks.

Theoretical analysis confirms ISP's increased expressivity and convergence properties.

Experiments show improved accuracy in graph and node classification, and influence estimation.

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.