Multi-Channel Graph Convolutions

Andreas Roth, Thomas Liebig

Keywords: graph convolution, spectral graph convolution, message-passing neural network

TL;DR: We introduce the convolution for multi-channel signals to graphs using the convolution theorem.

Abstract: Defining the convolution on graphs has led to much progress in graph machine learning, particularly through approximations based on polynomials and, ultimately, message-passing neural networks (MPNNs). However, this convolution is defined for single-channel graph signals, i.e., a single feature is given at each node, and a single new feature is assigned to each node. As multiple initial node features are provided for many challenging tasks and convolutions are generally defined for these multi-channel signals, we introduce multi-channel graph convolutions (MCGCs) by obtaining their form using the graph Fourier transform. MCGCs highlight the critical importance of utilizing multiple edge relations to amplify different signals for each feature channel. We further introduce localized multi-channel MPNNs and the multi-channel graph isomorphism network (MC-GINs), with which we can provably obtain linear mappings that are injective on multisets. Our experiments confirm the greatly improved capabilities of MCGCs and MC-GINs.

Primary Area: learning on graphs and other geometries & topologies

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 9759