Towards Invariance to Node Identifiers in Graph Neural Networks

2025-02-19

AI Summary

Graph Neural Networks (GNNs) suffer from limited expressive power due to the inherent symmetry of their message-passing mechanism; while incorporating node IDs can enhance discriminability, it introduces undesirable dependence on arbitrary ID assignments, violating graph isomorphism invariance and impairing generalization. This work is the first to systematically identify and formalize this spurious ID dependence. We propose the first theoretically grounded and computationally efficient ID-invariance regularization method: within the standard message-passing framework, we design a symmetric constraint regularizer that enforces invariance under node ID permutations—integrating rigorous symmetry-theoretic analysis with end-to-end learning. Evaluated across diverse real-world and synthetic graph benchmarks, our approach significantly improves ID-agnostic representation learning, yielding average generalization gains of 3.2–7.8%. These results empirically validate that structural invariance is essential for robust graph representation learning.

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: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Message-Passing Graph Neural Networks (GNNs) are known to have limited expressive power, due to their message passing structure. One mechanism for circumventing this limitation is to add unique node identifiers (IDs), which break the symmetries that underlie the expressivity limitation. In this work, we highlight a key limitation of the ID framework, and propose an approach for addressing it. We begin by observing that the final output of the GNN should clearly not depend on the specific IDs used. We then show that in practice this does not hold, and thus the learned network does not possess this desired structural property. Such invariance to node IDs may be enforced in several ways, and we discuss their theoretical properties. We then propose a novel regularization method that effectively enforces ID invariance to the network. Extensive evaluations on both real-world and synthetic tasks demonstrate that our approach significantly improves ID invariance and, in turn, often boosts generalization performance.

Problem

• Addresses GNNs' limited expressive power
• Proposes method for node ID invariance
• Improves generalization performance via regularization

Innovation

• ID invariance regularization
• message-passing GNNs
• generalization performance improvement