Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning

Abstract

In this paper, we provide a theory of using graph neural networks (GNNs) for multi-node representation learning (where we are interested in learning a representation for a set of more than one node, such as link). We know that GNN is designed to learn single-node representations. When we want to learn a node set representation involving multiple nodes, a common practice in previous works is to directly aggregate the single-node representations obtained by a GNN into a joint node set representation. In this paper, we show a fundamental constraint of such an approach, namely the inability to capture the dependence between nodes in the node set, and argue that directly aggregating individual node representations does not lead to an effective joint representation for multiple nodes. Then, we notice that a few previous successful works for multi-node representation learning, including SEAL, Distance Encoding, and ID-GNN, all used node labeling. These methods first label nodes in the graph according to their relationships with the target node set before applying a GNN. Then, the node representations obtained in the labeled graph are aggregated into a node set representation. By investigating their inner mechanisms, we unify these node labeling techniques into a single and most general form -- labeling trick. We prove that with labeling trick a sufficiently expressive GNN learns the most expressive node set representations, thus in principle solves any joint learning tasks over node sets. Experiments on one important two-node representation learning task, link prediction, verified our theory. Our work explains the superior performance of previous node-labeling-based methods, and establishes a theoretical foundation of using GNNs for multi-node representation learning.

Accepted to NeurIPS 2021

References in corpus (5)

• Semi-Supervised Classification with Graph Convolutional Networks
• Predicting Missing Links via Local Information
• Variational Graph Auto-Encoders
• Hyperbolic Graph Convolutional Neural Networks
• Principled Hyperedge Prediction with Structural Spectral Features and Neural Networks

Cited by in corpus (10)

• LPFormer: An Adaptive Graph Transformer for Link Prediction
• Pitfalls in Link Prediction with Graph Neural Networks: Understanding the Impact of Target-link Inclusion & Better Practices
• SUREL+: Moving from Walks to Sets for Scalable Subgraph-based Graph Representation Learning
• Improving the Expressiveness of $K$-hop Message-Passing GNNs by Injecting Contextualized Substructure Information
• BSAL: A Framework of Bi-component Structure and Attribute Learning for Link Prediction
• Learning Scalable Structural Representations for Link Prediction with Bloom Signatures
• Hierarchical Position Embedding of Graphs with Landmarks and Clustering for Link Prediction
• A Deep Latent Space Model for Graph Representation Learning
• Understanding the Design Principles of Link Prediction in Directed Settings
• LinkThief: Combining Generalized Structure Knowledge with Node Similarity for Link Stealing Attack against GNN