Multi-relational graph convolutional networks: Generalization guarantees and experiments

Xutao Li, Michael K. Ng, Guangning Xu, Andy Yip*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


The class of multi-relational graph convolutional networks (MRGCNs) is a recent extension of standard graph convolutional networks (GCNs) to handle heterogenous graphs with multiple types of relationships. MRGCNs have been shown to yield results superior than traditional GCNs in various machine learning tasks. The key idea is to introduce a new kind of convolution operated on tensors that can effectively exploit correlations exhibited in multiple relationships. The main objective of this paper is to analyze the algorithmic stability and generalization guarantees of MRGCNs to confirm the usefulness of MRGCNs. Our contributions are of three folds. First, we develop a matrix representation of various tensor operations underneath MRGCNs to simplify the analysis significantly. Next, we prove the uniform stability of MRGCNs and deduce the convergence of the generalization gap to support the usefulness of MRGCNs. The analysis sheds lights on the design of MRGCNs, for instance, how the data should be scaled to achieve the uniform stability of the learning process. Finally, we provide experimental results to demonstrate the stability results.

Original languageEnglish
Pages (from-to)343-358
Number of pages16
JournalNeural Networks
Early online date3 Feb 2023
Publication statusPublished - Apr 2023

Scopus Subject Areas

  • Cognitive Neuroscience
  • Artificial Intelligence

User-Defined Keywords

  • Algorithmic stability
  • Generalization guarantees
  • Graph convolutional networks
  • Multi-relational data


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