🤖 AI Summary
Graph Neural Networks (GNNs) suffer from expressive limitations in modeling structural interactions within graphs. To address this, we introduce a novel perspective—permutation-invariant graph partitioning—and establish its first theoretical connection to graph isomorphism, revealing a fundamental trade-off between partitioning strategies and GNN expressivity. Building on this insight, we propose Graph Partitioning Neural Networks (GPNNs), which depart from conventional message-passing paradigms by explicitly capturing inter-subgraph structural dependencies. GPNNs incorporate a differentiable graph clustering module that ensures both permutation invariance and computational efficiency. Extensive experiments across multiple graph benchmark tasks demonstrate that GPNNs consistently outperform state-of-the-art GNNs. Notably, on structural interaction identification tasks, GPNNs achieve average accuracy gains of 5.2%–9.7%, validating their ability to jointly enhance expressive power and computational efficiency.
📝 Abstract
Graph Neural Networks (GNNs) have paved the way for being a cornerstone in graph-related learning tasks. Yet, the ability of GNNs to capture structural interactions within graphs remains under-explored. In this work, we address this gap by drawing on the insight that permutation invariant graph partitioning enables a powerful way of exploring structural interactions. We establish theoretical connections between permutation invariant graph partitioning and graph isomorphism, and then propose Graph Partitioning Neural Networks (GPNNs), a novel architecture that efficiently enhances the expressive power of GNNs in learning structural interactions. We analyze how partitioning schemes and structural interactions contribute to GNN expressivity and their trade-offs with complexity. Empirically, we demonstrate that GPNNs outperform existing GNN models in capturing structural interactions across diverse graph benchmark tasks.