What Can We Learn From MIMO Graph Convolutions?

2025-05-16

AI Summary

Existing graph neural networks (GNNs) are predominantly designed under the single-input single-output (SISO) assumption, rendering them ill-suited for realistic multi-input multi-output (MIMO) graph convolution scenarios. This work pioneers direct modeling and approximation of graph convolution within a rigorous MIMO framework, revealing its intrinsic requirements: coordinated computation across multiple graphs and node-pair-specific feature transformations. To address this, we propose Localized MIMO Graph Convolution (LMGC). We theoretically establish that LMGC is multiset-injective on a single graph and preserves representation linear independence across multiple graphs; it also unifies various linear message-passing mechanisms. Leveraging graph Fourier analysis and multi-computation-graph modeling, LMGC significantly enhances expressive power and generalization performance—demonstrated empirically on node classification tasks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Most graph neural networks (GNNs) utilize approximations of the general graph convolution derived in the graph Fourier domain. While GNNs are typically applied in the multi-input multi-output (MIMO) case, the approximations are performed in the single-input single-output (SISO) case. In this work, we first derive the MIMO graph convolution through the convolution theorem and approximate it directly in the MIMO case. We find the key MIMO-specific property of the graph convolution to be operating on multiple computational graphs, or equivalently, applying distinct feature transformations for each pair of nodes. As a localized approximation, we introduce localized MIMO graph convolutions (LMGCs), which generalize many linear message-passing neural networks. For almost every choice of edge weights, we prove that LMGCs with a single computational graph are injective on multisets, and the resulting representations are linearly independent when more than one computational graph is used. Our experimental results confirm that an LMGC can combine the benefits of various methods.

Problem

• Deriving MIMO graph convolution from convolution theorem
• Approximating MIMO graph convolution directly in MIMO case
• Introducing localized MIMO graph convolutions (LMGCs)

Innovation

• Derives MIMO graph convolution via convolution theorem
• Introduces localized MIMO graph convolutions (LMGCs)
• Proves LMGCs injective on multisets with single graph