Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization

Arie Soeteman, Balder ten Cate

Keywords: Graph Neural Networks, Hybrid Logic, Individualization-Refinement

TL;DR: We study the separating power of Hierarchical Ego GNNs through graded hybrid logic characterizations.

Abstract: We propose and study Hierarchical Ego Graph Neural Networks (HE-GNNs), an expressive extension of graph neural networks (GNNs) with hierarchical node individualization, inspired by the Individualization-Refinement paradigm for isomorphism testing. HE-GNNs generalize subgraph-GNNs and form a hierarchy of increasingly expressive models that, in the limit, distinguish graphs up to isomorphism. We show that, over graphs of bounded degree, the separating power of HE-GNN node classifiers equals that of graded hybrid logic. This characterization enables us to relate the separating power of HE-GNNs 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 HE-GNNs and show benefits in comparison with traditional GNN architectures, both with and without local homomorphism count features.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 17665