Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization

2025-06-16

AI Summary

Graph neural networks (GNNs) are fundamentally limited in expressive power by their inability to distinguish non-isomorphic graphs—i.e., the graph isomorphism problem. To address this, we propose Hierarchical Ego-centric Graph Neural Networks (HEGNN), the first GNN architecture to incorporate the “individualization-refinement” paradigm from combinatorial algorithms. HEGNN employs a hierarchical node individualization mechanism, multi-level hybrid logical representations, and local homomorphism-aware feature aggregation, enabling progressive discrimination—from subgraph modeling to fine-grained graph isomorphism testing. Theoretically, we prove that HEGNN is expressively equivalent to higher-order GNNs, color refinement algorithms, and local homomorphism counting logic. Empirically, HEGNN achieves significant improvements over standard GNNs across diverse graph learning benchmarks, demonstrating superior isomorphism sensitivity, trainability, and practical generalization performance.

Technology Category

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

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

We propose and study Hierarchical Ego Graph Neural Networks (HEGNNs), an expressive extension of graph neural networks (GNNs) with hierarchical node individualization, inspired by the Individualization-Refinement paradigm for graph isomorphism testing. HEGNNs generalize subgraph-GNNs and form a hierarchy of increasingly expressive models that, in the limit, can distinguish graphs up to isomorphism. We provide a logical characterization of HEGNN node classifiers, with and without subgraph restrictions, using graded hybrid logic. This characterization enables us to relate the separating power of HEGNNs to that of higher-order GNNs, GNNs enriched with local homomorphism count features, and color refinement algorithms based on Individualization-Refinement. Our experimental results confirm the practical feasibility of HEGNNs and show benefits in comparison with traditional GNN architectures, both with and without local homomorphism count features.

Problem

• Extending GNN expressiveness via hierarchical node individualization
• Characterizing HEGNNs' logical power using graded hybrid logic
• Comparing HEGNNs with traditional GNN architectures experimentally

Innovation

• HEGNNs extend GNNs with hierarchical node individualization
• Logical characterization using graded hybrid logic
• Experimental validation shows practical feasibility and benefits